Financial mathematics 111 Chapter four: Annuities Bank اسم الطالب:... رقم الطالب:... الصف:... المدرسة:... الرقم التسلسلي
Chapter Four: Annuities:. KEY TERM INTRODUCED: متساویة.. Equal دفعات. Annuity مدة السداد payment Term of the فترة السداد period Payment Payments السداد Sum number payment العادیة... Ordinary الاستثمار.... Investment مجموع دفعات السداد تخفیض.. Detecting قیمة value عناصر.... Factory قرض.. Loan فسحة السداد interval Payment تغییر Confer Types of annuities: First: Payment annuities:. (Ordinary annuities) Example: Suppose there are four annuities deposits of BD100 at the end of each year, will be made to an account paying 7% annually, starting a year from now. What will be the amount at the end of four years? Paid BD 100 at the end of each year BD 100 BD 100 BD 100 BD 100 0 1 st year 1 2 nd year 2 3 rd year 3 4 th year 4 CA=100(1+0.07) 3 = BD 122.504 CA=100(1+0.07) 2 = BD 114.490 CA=100(1+0.07) 1 = BD 107.000 0 CA=100(1+0.07) = BD 100.000 Total Sn = BD 443.994 Second: investment annuities:. (Due annuities) Example: Suppose five annuities deposits of BD100 at the beginning of each year, will be made to an account paying 7 % annually, starting a year from now. What will be the amount at the end of four years? Paid BD100 at the beginning of each year BD 100 BD 100 BD 100 0 1 st year 1 2 nd year 2 3 rd year 3 4 th year 4 Uploaded by: Ayman Ayyad (Danger3) 2 BD 100 CA=100(1+0.07) 4 = BD 131.080 CA=100(1+0.07) 3 = BD 122.504 CA=100(1+0.07) 2 = BD 114.490 CA=100(1+0.07) = BD 107.000 Total Sn = BD 475.074 Prepared by T: A. JALIL ALAIWI 1
**Note: 1- If we don t have table 3 or the number of payment more than 50 we could find the amount of payment by using a low only. Uploaded by: Ayman Ayyad (Danger3) 3 Prepared by T: A. JALIL ALAIWI
2- Sn of Investment Annuities = Sn of Payment annuities x (1+i). Exercise 1: A man paid an annuity of BD150 at the each year for 3 years at an interest rate of 5% annually. Find the compounded amount and interest of two types of annuity. Payment annuities (Ordinary annuities) Investment Annuities (Due annuities) Exercise 2: Calculate the compound amount & interest of an ordinary annuity of BD200 paid 4 times a year for 6 years if the nominal rate is 4%? Uploaded by: Ayman Ayyad (Danger3) 4 Prepared by T: A. JALIL ALAIWI
Exercise 3: Sultan invests an annuity of BD 80 at the beginning of every third year for 2 years and 8 months at 3¼% thirdly.find the balance of the annuities and the interest? Exercise 5: Jalal deposited at the end of each year BD150 in a bank for 10 years at an interest of 5.5% annually. Find the following: a) The amount b) The interest? Uploaded by: Ayman Ayyad (Danger3) 5 Prepared by T: A. JALIL ALAIWI
Exercise 6: Nadia paid at the beginning of each year 80 for six years at a nominal rate of 4% find the compound interest. Exercise 7: Calculate the amount of BD400 due annuities paid every quarter year for 10 years and 3 months at 2.5% quarterly? Uploaded by: Ayman Ayyad (Danger3) 6 Prepared by T: A. JALIL ALAIWI
Exercise 8: A man started to invest for his child from the day he was born for BD400 at the beginning of every half year at 6% annually. How much will he earn when his child reaches 18 years old? Exercise 9: Khalifa paid at the end of each year BD1000 in a fund that earns an interest of 3¼% annually find how much his fund will generate after 5 years? Exercise 10: Sajeda deposits BD125 at the beginning of every quarter in a savings fund that earns interest at the rate 2½% semi-annually. How much will be in her account at the end of 12 years if she has BD5,500 in the fund at the present. Uploaded by: Ayman Ayyad (Danger3) 7 Prepared by T: A. JALIL ALAIWI
Exercise 11: Badrya pays BD150 at the end of each month for 3 years at interest of 3% each month. What is the amount of this payment at the end of the period? Uploaded by: Ayman Ayyad (Danger3) 8 Prepared by T: A. JALIL ALAIWI
Finding the value of annuity:. Exercise 12: Amal pays a loan at the end of each year for 10 years at 5 % annually. If the compound amount of annuities at the end of the period was BD1006.232 - what is the value of each ordinary annuity? Exercise 13: What quarterly deposit will accumulate to BD2767.650 in five years at 12 % annually compounded quarterly? Uploaded by: Ayman Ayyad (Danger3) 9 Prepared by T: A. JALIL ALAIWI
Exercise 14: Sajeda deposits a sum of money at the beginning of each year at 4% annually and the amount of annuity became BD1872.96 after 10 years.what was the value of each annuity? Exercise 15: Awatef paid at the end of each year sum of money at 2% annually so that the amount of annuities after 11 years was BD973.496. What was the value of each annuity? Exercise 16: Qassim deposits an equal annuity at the beginning of each year in his fund. The compound interest rate is 2.5% per annum and his balance at the end of 10 years was BD 746.428.Find the value of each annuity? Uploaded by: Ayman Ayyad (Danger3) 10 Prepared by T: A. JALIL ALAIWI
Exercise 17: At the beginning of every 4 months Nasser deposited an annuity in a bank for 7 years at 9% annually. If the accumulated fund for him became $ 3249.048.Find how much Nasser deposited every 4 months? Exercise 18: Rayan deposited at the middle and at the end of each year an equal payment for 10 years at 5% annually. If the total amount of annuities at the end of the period was BD5236.664. Find the value of each annuity? Exercise 19: What semi annually payment will accumulate to BD1080.549 in five years at 8% annually compounded semi- annually? Uploaded by: Ayman Ayyad (Danger3) 11 Prepared by T: A. JALIL ALAIWI
Exercise 20: Bilal paid an annuity every year at 6% annually if the amount of annuities after 10 years was BD922.656. Find the value of each annuity? Uploaded by: Ayman Ayyad (Danger3) 12 Prepared by T: A. JALIL ALAIWI
Finding the interest rate:. Exercise 21: A man deposited BD600 at the end of every 6 months. After 6 years and 6 months he earns a total amount of annuities BD10,375.123 find the semi- annually rate? Exercise 22: Fatima paid at the end of every 3 months BD 500 for 8 years if the total amount was BD31350.75.Find the nominal rate? Exercise 23: Fouad pays at the end of each year BD 180, after 20 years the total amount of the annuities was BD 6988.554 Find the rate of the compound interest? Uploaded by: Ayman Ayyad (Danger3) 13 Prepared by T: A. JALIL ALAIWI
Exercise 24: Omran pays at the end of each year BD200. If the total compound interest at the end of 4 years BD141.940. Find his balance at the end of 4 years and the compound interest rate? Exercise 25: Waheed invests BD80 at the beginning of each year; his total amount after 10 years was BD 1117.728. Find the compound interest rate? Uploaded by: Ayman Ayyad (Danger3) 14 Prepared by T: A. JALIL ALAIWI
Exercise 26: Find the nominal rate of interest for BD150 deposit at the beginning of every quarter year for 6 years and 3 months will amount to BD5,632.950? Exercise 27: Shehab deposited at the beginning of every 3 months BD500. If the total amount after 3 years became BD7,813.420 find the compound interest rate and the total compound interest?. Uploaded by: Ayman Ayyad (Danger3) 15 Prepared by T: A. JALIL ALAIWI
Exercise 28: Salman deposited in a bank at the beginning of every year BD1,000 and the fund was accumulated for him at the end of 20 years was BD32783.113 -Find the compound interest rate? Uploaded by: Ayman Ayyad (Danger3) 16 Prepared by T: A. JALIL ALAIWI
Finding Time/Number Exercise 29: How many number of payment we have to deposit in a bank at the end of each year to earn BD7,008.260 as a amount of annuity if you know that the value of each annuity was BD 350 and the compound interest rate was 4% annually? Exercise 30: How long will it take for BD120 paid at the end of each year to amount of BD3967.920 at 5% annually? Uploaded by: Ayman Ayyad (Danger3) 17 Prepared by T: A. JALIL ALAIWI
Exercise 31 Yousif deposits BD340 at the end of each 4 months at 9% annually. He earns total amount annuities of B4825.280 - Find the number of payments? Exercise 32: Najla paid BD500 at the end of each year at 5.5% annually. Find the number of annuities accumulated for her BD8192.800? Exercise 33: How long will it take for BD 45 deposited at the end of each 4 months to be BD1706.040 at the rate of 2.5% every 4 months? Uploaded by: Ayman Ayyad (Danger3) 18 Prepared by T: A. JALIL ALAIWI
.. Exercise 34: How long would it take BD50 deposited at the beginning of each semi- annually to become to BD660.340 at 10 % annually? Exercise 35: How long will take BD120 deposits at the beginning of every year to amount BD 1149.936 at 4% annual rate? Uploaded by: Ayman Ayyad (Danger3) 19 Prepared by T: A. JALIL ALAIWI
Exercise 36: Zuhair deposited BD600 at the beginning of every 4 months at a compound interest rate of 7.5% annually. The total amount at the end of the period was BD11028.120, find the: A- Number of payments B- Time of annuities C- Compound interest. Exercise 37 Nasser wishes to borrow BD9275.220 for repairing his house; he can pay BD150 at the beginning of each month at 12% annually. Find how many annuities must he pay through There years? Uploaded by: Ayman Ayyad (Danger3) 20 Prepared by T: A. JALIL ALAIWI
Uploaded by: Ayman Ayyad (Danger3) 21 Prepared by T: A. JALIL ALAIWI
1. Find the value of the following: A- 15 6% B- 62 7.5% General Exercise 1. At the beginning of every 4 months Fatima deposited an annuity in a bank at 3% annual rate and accumulated fund for her became BD 2179.456 after 8 years. Find how much Fatima deposited every 4 months? 2. A man deposited BD 1,000 at the end of each year for 5 years if the fund accumulated for him was BD 5866.600 Find the nominal rate and the compound interest? 3. Find the compound interest rate at which BD560 paid at the end of each quarter for 8 years will amount to BD1,9380.816? 4. Sameera deposited BD600 in a bank at the end of every 6 months for 10 years if the fund accumulated for her was BD24597.3.Find the compound interest rate? 5. Alya deposited at the beginning of each year BD600. The amount of the annuities after 12 years was BD10,729.26. Find the compound interest rate? 6. A man pays BD70 at the end of each year. His total amount after 15 years was BD1350.699. Find the compound interest rate? 7. How long will it take for BD900 that deposited in a bank at the end of each year at 6% to amount to BD18913.59? 8. How long will it take BD 400 to become amount of BD3,959 at 6%annually? Uploaded by: Ayman Ayyad (Danger3) 22 Prepared by T: A. JALIL ALAIWI
INTEREST TABLES OF ANNUITIES TABLE No.3 Equation : SN =[(1+ i) N -1] / i SN for one monetary unit N 0.5% 0.75% 1% 1.25% 1.5% 1.75% 2% 2.25% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0050 2.0075 2.0100 2.0125 2.0150 2.0175 2.0200 2.0225 3 3.0150 3.0226 3.0301 3.0377 3.0452 3.0528 3.0604 3.0680 4 4.0301 4.0452 4.0604 4.0756 4.0909 4.1062 4.1216 4.1370 5 5.0503 5.0756 5.1010 5.1266 5.1523 5.1781 5.2040 5.2301 6 6.0755 6.1136 6.1520 6.1907 6.2296 6.2687 6.3081 6.3478 7 7.1059 7.1595 7.2135 7.2680 7.3230 7.3784 7.4343 7.4906 8 8.1414 8.2132 8.2857 8.3589 8.4328 8.5075 8.5830 8.6592 9 9.1821 9.2748 9.3685 9.4634 9.5593 9.6564 9.7546 9.8540 10 10.2280 10.3443 10.4622 10.5817 10.7027 10.8254 10.9497 11.0757 11 11.2792 11.4219 11.5668 11.7139 11.8633 12.0148 12.1687 12.3249 12 12.3356 12.5076 12.6825 12.8604 13.0412 13.2251 13.4121 13.6022 13 13.3972 13.6014 13.8093 14.0211 14.2368 14.4565 14.6803 14.9083 14 14.4642 14.7034 14.9474 15.1964 15.4504 15.7095 15.9739 16.2437 15 15.5365 15.8137 16.0969 16.3863 16.6821 16.9844 17.2934 17.6092 16 16.6142 16.9323 17.2579 17.5912 17.9324 18.2817 18.6393 19.0054 17 17.6973 18.0593 18.4304 18.8111 19.2014 19.6016 20.0121 20.4330 18 18.7858 19.1947 19.6147 20.0462 20.4894 20.9446 21.4123 21.8928 19 19.8797 20.3387 20.8109 21.2968 21.7967 22.3112 22.8406 23.3853 20 20.9791 21.4912 22.0190 22.5630 23.1237 23.7016 24.2974 24.9115 21 22.0840 22.6524 23.2392 23.8450 24.4705 25.1164 25.7833 26.4720 22 23.1944 23.8223 24.4716 25.1431 25.8376 26.5559 27.2990 28.0676 23 24.3104 25.0010 25.7163 26.4574 27.2251 28.0207 28.8450 29.6992 24 25.4320 26.1885 26.9735 27.7881 28.6335 29.5110 30.4219 31.3674 25 26.5591 27.3849 28.2432 29.1354 30.0630 31.0275 32.0303 33.0732 26 27.6919 28.5903 29.5256 30.4996 31.5140 32.5704 33.6709 34.8173 27 28.8304 29.8047 30.8209 31.8809 32.9867 34.1404 35.3443 36.6007 28 29.9745 31.0282 32.1291 33.2794 34.4815 35.7379 37.0512 38.4242 29 31.1244 32.2609 33.4504 34.6954 35.9987 37.3633 38.7922 40.2888 30 32.2800 33.5029 34.7849 36.1291 37.5387 39.0172 40.5681 42.1953 31 33.4414 34.7542 36.1327 37.5807 39.1018 40.7000 42.3794 44.1447 32 34.6086 36.0148 37.4941 39.0504 40.6883 42.4122 44.2270 46.1379 33 35.7817 37.2849 38.8690 40.5386 42.2986 44.1544 46.1116 48.1760 34 36.9606 38.5646 40.2577 42.0453 43.9331 45.9271 48.0338 50.2600 35 38.1454 39.8538 41.6603 43.5709 45.5921 47.7308 49.9945 52.3908 36 39.3361 41.1527 43.0769 45.1155 47.2760 49.5661 51.9944 54.5696 37 40.5328 42.4614 44.5076 46.6794 48.9851 51.4335 54.0343 56.7974 38 41.7354 43.7798 45.9527 48.2629 50.7199 53.3336 56.1149 59.0754 39 42.9441 45.1082 47.4123 49.8662 52.4807 55.2670 58.2372 61.4046 40 44.1588 46.4465 48.8864 51.4896 54.2679 57.2341 60.4020 63.7862 41 45.3796 47.7948 50.3752 53.1332 56.0819 59.2357 62.6100 66.2214 42 46.6065 49.1533 51.8790 54.7973 57.9231 61.2724 64.8622 68.7113 43 47.8396 50.5219 53.3978 56.4823 59.7920 63.3446 67.1595 71.2574 44 49.0788 51.9009 54.9318 58.1883 61.6889 65.4532 69.5027 73.8606 45 50.3242 53.2901 56.4811 59.9157 63.6142 67.5986 71.8927 76.5225 46 51.5758 54.6898 58.0459 61.6646 65.5684 69.7816 74.3306 79.2443 47 52.8337 56.1000 59.6263 63.4354 67.5519 72.0027 76.8172 82.0273 48 54.0978 57.5207 61.2226 65.2284 69.5652 74.2628 79.3535 84.8729 49 55.3683 58.9521 62.8348 67.0437 71.6087 76.5624 81.9406 87.7825 50 56.6452 60.3943 64.4632 68.8818 73.6828 78.9022 84.5794 90.7576 Uploaded by: Ayman Ayyad (Danger3) 23 Prepared by T: A. JALIL ALAIWI
TABLE No.3 Equation : SN =[(1+ i) N -1] / i SN for one monetary unit N 2.5% 2.75% 3% 3.25% 3.5% 3.75% 4% 4.25% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0250 2.0275 2.0300 2.0325 2.0350 2.0375 2.0400 2.0425 3 3.0756 3.0833 3.0909 3.0986 3.1062 3.1139 3.1216 3.1293 4 4.1525 4.1680 4.1836 4.1993 4.2149 4.2307 4.2465 4.2623 5 5.2563 5.2827 5.3091 5.3357 5.3625 5.3893 5.4163 5.4434 6 6.3877 6.4279 6.4684 6.5091 6.5502 6.5914 6.6330 6.6748 7 7.5474 7.6047 7.6625 7.7207 7.7794 7.8386 7.8983 7.9585 8 8.7361 8.8138 8.8923 8.9716 9.0517 9.1326 9.2142 9.2967 9 9.9545 10.0562 10.1591 10.2632 10.3685 10.4750 10.5828 10.6918 10 11.2034 11.3328 11.4639 11.5967 11.7314 11.8678 12.0061 12.1462 11 12.4835 12.6444 12.8078 12.9736 13.1420 13.3129 13.4864 13.6624 12 13.7956 13.9921 14.1920 14.3953 14.6020 14.8121 15.0258 15.2431 13 15.1404 15.3769 15.6178 15.8631 16.1130 16.3676 16.6268 16.8909 14 16.5190 16.7998 17.0863 17.3787 17.6770 17.9814 18.2919 18.6088 15 17.9319 18.2618 18.5989 18.9435 19.2957 19.6557 20.0236 20.3997 16 19.3802 19.7640 20.1569 20.5592 20.9710 21.3927 21.8245 22.2666 17 20.8647 21.3075 21.7616 22.2273 22.7050 23.1950 23.6975 24.2130 18 22.3863 22.8934 23.4144 23.9497 24.4997 25.0648 25.6454 26.2420 19 23.9460 24.5230 25.1169 25.7281 26.3572 27.0047 27.6712 28.3573 20 25.5447 26.1974 26.8704 27.5642 28.2797 29.0174 29.7781 30.5625 21 27.1833 27.9178 28.6765 29.4601 30.2695 31.1055 31.9692 32.8614 22 28.8629 29.6856 30.5368 31.4175 32.3289 33.2720 34.2480 35.2580 23 30.5844 31.5019 32.4529 33.4386 34.4604 35.5197 36.6179 37.7565 24 32.3490 33.3682 34.4265 35.5254 36.6665 37.8517 39.0826 40.3611 25 34.1578 35.2858 36.4593 37.6799 38.9499 40.2711 41.6459 43.0765 26 36.0117 37.2562 38.5530 39.9045 41.3131 42.7813 44.3117 45.9072 27 37.9120 39.2808 40.7096 42.2014 43.7591 45.3856 47.0842 48.8583 28 39.8598 41.3610 42.9309 44.5730 46.2906 48.0875 49.9676 51.9348 29 41.8563 43.4984 45.2189 47.0216 48.9108 50.8908 52.9663 55.1420 30 43.9027 45.6946 47.5754 49.5498 51.6227 53.7992 56.0849 58.4855 31 46.0003 47.9512 50.0027 52.1602 54.4295 56.8167 59.3283 61.9712 32 48.1503 50.2699 52.5028 54.8554 57.3345 59.9473 62.7015 65.6049 33 50.3540 52.6523 55.0778 57.6382 60.3412 63.1954 66.2095 69.3931 34 52.6129 55.1002 57.7302 60.5114 63.4532 66.5652 69.8579 73.3424 35 54.9282 57.6155 60.4621 63.4780 66.6740 70.0614 73.6522 77.4594 36 57.3014 60.1999 63.2759 66.5411 70.0076 73.6887 77.5983 81.7514 37 59.7339 62.8554 66.1742 69.7037 73.4579 77.4520 81.7022 86.2259 38 62.2273 65.5839 69.1594 72.9690 77.0289 81.3565 85.9703 90.8905 39 64.7830 68.3875 72.2342 76.3405 80.7249 85.4073 90.4091 95.7533 40 67.4026 71.2681 75.4013 79.8216 84.5503 89.6101 95.0255 100.8228 41 70.0876 74.2280 78.6633 83.4158 88.5095 93.9705 99.8265 106.1078 42 72.8398 77.2693 82.0232 87.1268 92.6074 98.4944 104.8196 111.6174 43 75.6608 80.3942 85.4839 90.9584 96.8486 103.1879 110.0124 117.3611 44 78.5523 83.6050 89.0484 94.9146 101.2383 108.0575 115.4129 123.3490 45 81.5161 86.9042 92.7199 98.9993 105.7817 113.1096 121.0294 129.5913 46 84.5540 90.2940 96.5015 103.2168 110.4840 118.3512 126.8706 136.0989 47 87.6679 93.7771 100.3965 107.5713 115.3510 123.7894 132.9454 142.8831 48 90.8596 97.3560 104.4084 112.0674 120.3883 129.4315 139.2632 149.9557 49 94.1311 101.0333 108.5406 116.7096 125.6018 135.2852 145.8337 157.3288 50 97.4843 104.8117 112.7969 121.5026 130.9979 141.3584 152.6671 165.0153 Uploaded by: Ayman Ayyad (Danger3) 24 Prepared by T: A. JALIL ALAIWI
TABLE No.3 Equation : SN =[(1+ i) N -1] / i SN for one monetary unit N 4.5% 4.75% 5% 5.25% 5.5% 5.75% 6% 6.25% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0450 2.0475 2.0500 2.0525 2.0550 2.0575 2.0600 2.0625 3 3.1370 3.1448 3.1525 3.1603 3.1680 3.1758 3.1836 3.1914 4 4.2782 4.2941 4.3101 4.3262 4.3423 4.3584 4.3746 4.3909 5 5.4707 5.4981 5.5256 5.5533 5.5811 5.6090 5.6371 5.6653 6 6.7169 6.7593 6.8019 6.8448 6.8881 6.9315 6.9753 7.0194 7 8.0192 8.0803 8.1420 8.2042 8.2669 8.3301 8.3938 8.4581 8 9.3800 9.4641 9.5491 9.6349 9.7216 9.8091 9.8975 9.9867 9 10.8021 10.9137 11.0266 11.1407 11.2563 11.3731 11.4913 11.6109 10 12.2882 12.4321 12.5779 12.7256 12.8754 13.0271 13.1808 13.3366 11 13.8412 14.0226 14.2068 14.3937 14.5835 14.7761 14.9716 15.1701 12 15.4640 15.6887 15.9171 16.1494 16.3856 16.6257 16.8699 17.1182 13 17.1599 17.4339 17.7130 17.9972 18.2868 18.5817 18.8821 19.1881 14 18.9321 19.2620 19.5986 19.9421 20.2926 20.6502 21.0151 21.3874 15 20.7841 21.1770 21.5786 21.9891 22.4087 22.8376 23.2760 23.7241 16 22.7193 23.1829 23.6575 24.1435 24.6411 25.1507 25.6725 26.2069 17 24.7417 25.2840 25.8404 26.4110 26.9964 27.5969 28.2129 28.8448 18 26.8551 27.4850 28.1324 28.7976 29.4812 30.1837 30.9057 31.6476 19 29.0636 29.7906 30.5390 31.3095 32.1027 32.9193 33.7600 34.6256 20 31.3714 32.2056 33.0660 33.9532 34.8683 35.8121 36.7856 37.7897 21 33.7831 34.7354 35.7193 36.7358 37.7861 38.8713 39.9927 41.1515 22 36.3034 37.3853 38.5052 39.6644 40.8643 42.1064 43.3923 44.7235 23 38.9370 40.1611 41.4305 42.7468 44.1118 45.5275 46.9958 48.5187 24 41.6892 43.0688 44.5020 45.9910 47.5380 49.1454 50.8156 52.5511 25 44.5652 46.1146 47.7271 49.4055 51.1526 52.9712 54.8645 56.8356 26 47.5706 49.3050 51.1135 52.9993 54.9660 57.0171 59.1564 61.3878 27 50.7113 52.6470 54.6691 56.7818 58.9891 61.2956 63.7058 66.2245 28 53.9933 56.1477 58.4026 60.7628 63.2335 65.8201 68.5281 71.3635 29 57.4230 59.8147 62.3227 64.9529 67.7114 70.6047 73.6398 76.8238 30 61.0071 63.6559 66.4388 69.3629 72.4355 75.6645 79.0582 82.6253 31 64.7524 67.6796 70.7608 74.0044 77.4194 81.0152 84.8017 88.7893 32 68.6662 71.8944 75.2988 78.8897 82.6775 86.6736 90.8898 95.3387 33 72.7562 76.3094 80.0638 84.0314 88.2248 92.6573 97.3432 102.2973 34 77.0303 80.9341 85.0670 89.4430 94.0771 98.9851 104.1838 109.6909 35 81.4966 85.7784 90.3203 95.1388 100.2514 105.6767 111.4348 117.5466 36 86.1640 90.8529 95.8363 101.1336 106.7652 112.7532 119.1209 125.8933 37 91.0413 96.1684 101.6281 107.4431 113.6373 120.2365 127.2681 134.7616 38 96.1382 101.7364 107.7095 114.0838 120.8873 128.1501 135.9042 144.1842 39 101.4644 107.5689 114.0950 121.0732 128.5361 136.5187 145.0585 154.1957 40 107.0303 113.6784 120.7998 128.4296 136.6056 145.3685 154.7620 164.8329 41 112.8467 120.0781 127.8398 136.1721 145.1189 154.7272 165.0477 176.1350 42 118.9248 126.7818 135.2318 144.3212 154.1005 164.6240 175.9505 188.1434 43 125.2764 133.8040 142.9933 152.8980 163.5760 175.0899 187.5076 200.9024 44 131.9138 141.1597 151.1430 161.9252 173.5727 186.1576 199.7580 214.4588 45 138.8500 148.8648 159.7002 171.4262 184.1192 197.8616 212.7435 228.8625 46 146.0982 156.9358 168.6852 181.4261 195.2457 210.2387 226.5081 244.1664 47 153.6726 165.3903 178.1194 191.9510 206.9842 223.3274 241.0986 260.4268 48 161.5879 174.2463 188.0254 203.0284 219.3684 237.1687 256.5645 277.7034 49 169.8594 183.5230 198.4267 214.6874 232.4336 251.8059 272.9584 296.0599 50 178.5030 193.2404 209.3480 226.9585 246.2175 267.2848 290.3359 315.5637 Uploaded by: Ayman Ayyad (Danger3) 25 Prepared by T: A. JALIL ALAIWI
TABLE No.3 Equation : SN =[(1+ i) N -1] / i SN for one monetary unit N 6.5% 6.75% 7% 7.25% 7.5% 7.75% 8% 8.25% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0650 2.0675 2.0700 2.0725 2.0750 2.0775 2.0800 2.0825 3 3.1992 3.2071 3.2149 3.2228 3.2306 3.2385 3.2464 3.2543 4 4.4072 4.4235 4.4399 4.4564 4.4729 4.4895 4.5061 4.5228 5 5.6936 5.7221 5.7507 5.7795 5.8084 5.8374 5.8666 5.8959 6 7.0637 7.1084 7.1533 7.1985 7.2440 7.2898 7.3359 7.3823 7 8.5229 8.5882 8.6540 8.7204 8.7873 8.8548 8.9228 8.9914 8 10.0769 10.1679 10.2598 10.3526 10.4464 10.5410 10.6366 10.7332 9 11.7319 11.8542 11.9780 12.1032 12.2298 12.3580 12.4876 12.6186 10 13.4944 13.6544 13.8164 13.9807 14.1471 14.3157 14.4866 14.6597 11 15.3716 15.5760 15.7836 15.9943 16.2081 16.4252 16.6455 16.8691 12 17.3707 17.6274 17.8885 18.1539 18.4237 18.6981 18.9771 19.2608 13 19.4998 19.8173 20.1406 20.4700 20.8055 21.1472 21.4953 21.8498 14 21.7673 22.1549 22.5505 22.9541 23.3659 23.7861 24.2149 24.6524 15 24.1822 24.6504 25.1290 25.6183 26.1184 26.6296 27.1521 27.6863 16 26.7540 27.3143 27.8881 28.4756 29.0772 29.6934 30.3243 30.9704 17 29.4930 30.1580 30.8402 31.5401 32.2580 32.9946 33.7502 34.5254 18 32.4101 33.1937 33.9990 34.8267 35.6774 36.5517 37.4502 38.3738 19 35.5167 36.4343 37.3790 38.3517 39.3532 40.3844 41.4463 42.5396 20 38.8253 39.8936 40.9955 42.1322 43.3047 44.5142 45.7620 47.0491 21 42.3490 43.5864 44.8652 46.1867 47.5525 48.9641 50.4229 51.9307 22 46.1016 47.5285 49.0057 50.5353 52.1190 53.7588 55.4568 57.2150 23 50.0982 51.7366 53.4361 55.1991 57.0279 58.9251 60.8933 62.9352 24 54.3546 56.2289 58.1767 60.2010 62.3050 64.4918 66.7648 69.1274 25 58.8877 61.0243 63.2490 65.5656 67.9779 70.4899 73.1059 75.8304 26 63.7154 66.1435 68.6765 71.3191 74.0762 76.9529 79.9544 83.0864 27 68.8569 71.6081 74.4838 77.4897 80.6319 83.9167 87.3508 90.9410 28 74.3326 77.4417 80.6977 84.1077 87.6793 91.4203 95.3388 99.4436 29 80.1642 83.6690 87.3465 91.2055 95.2553 99.5053 103.9659 108.6477 30 86.3749 90.3167 94.4608 98.8179 103.3994 108.2170 113.2832 118.6112 31 92.9892 97.4130 102.0730 106.9823 112.1544 117.6038 123.3459 129.3966 32 100.0335 104.9884 110.2182 115.7385 121.5659 127.7181 134.2135 141.0718 33 107.5357 113.0751 118.9334 125.1295 131.6834 138.6163 145.9506 153.7102 34 115.5255 121.7077 128.2588 135.2014 142.5596 150.3590 158.6267 167.3913 35 124.0347 130.9230 138.2369 146.0035 154.2516 163.0118 172.3168 182.2011 36 133.0969 140.7603 148.9135 157.5887 166.8205 176.6453 187.1021 198.2327 37 142.7482 151.2616 160.3374 170.0139 180.3320 191.3353 203.0703 215.5869 38 153.0269 162.4717 172.5610 183.3399 194.8569 207.1638 220.3159 234.3728 39 163.9736 174.4386 185.6403 197.6321 210.4712 224.2190 238.9412 254.7086 40 175.6319 187.2132 199.6351 212.9604 227.2565 242.5959 259.0565 276.7221 41 188.0480 200.8501 214.6096 229.4000 245.3008 262.3971 280.7810 300.5516 42 201.2711 215.4075 230.6322 247.0315 264.6983 283.7329 304.2435 326.3471 43 215.3537 230.9475 247.7765 265.9413 285.5507 306.7222 329.5830 354.2708 44 230.3517 247.5364 266.1209 286.2221 307.9670 331.4931 356.9496 384.4981 45 246.3246 265.2451 285.7493 307.9732 332.0645 358.1839 386.5056 417.2192 46 263.3357 284.1492 306.7518 331.3012 357.9694 386.9431 418.4261 452.6398 47 281.4525 304.3292 329.2244 356.3206 385.8171 417.9312 452.9002 490.9826 48 300.7469 325.8715 353.2701 383.1538 415.7533 451.3209 490.1322 532.4886 49 321.2955 348.8678 378.9990 411.9325 447.9348 487.2982 530.3427 577.4190 50 343.1797 373.4164 406.5289 442.7976 482.5299 526.0639 573.7702 626.0560 Uploaded by: Ayman Ayyad (Danger3) 26 Prepared by T: A. JALIL ALAIWI
TABLE No.3 N Equation : SN =[(1+ i) -1] / i SN for one monetary unit N 8.5% 8.75% 9% 9.25% 9.5% 9.75% 10% 10.25% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0850 2.0875 2.0900 2.0925 2.0950 2.0975 2.1000 2.1025 3 3.2622 3.2702 3.2781 3.2861 3.2940 3.3020 3.3100 3.3180 4 4.5395 4.5563 4.5731 4.5900 4.6070 4.6240 4.6410 4.6581 5 5.9254 5.9550 5.9847 6.0146 6.0446 6.0748 6.1051 6.1356 6 7.4290 7.4760 7.5233 7.5709 7.6189 7.6671 7.7156 7.7645 7 9.0605 9.1302 9.2004 9.2713 9.3426 9.4146 9.4872 9.5603 8 10.8306 10.9291 11.0285 11.1288 11.2302 11.3325 11.4359 11.5402 9 12.7512 12.8854 13.0210 13.1583 13.2971 13.4375 13.5795 13.7231 10 14.8351 15.0128 15.1929 15.3754 15.5603 15.7476 15.9374 16.1297 11 17.0961 17.3265 17.5603 17.7976 18.0385 18.2830 18.5312 18.7830 12 19.5492 19.8425 20.1407 20.4439 20.7522 21.0656 21.3843 21.7083 13 22.2109 22.5787 22.9534 23.3350 23.7236 24.1195 24.5227 24.9334 14 25.0989 25.5544 26.0192 26.4935 26.9774 27.4712 27.9750 28.4891 15 28.2323 28.7904 29.3609 29.9441 30.5402 31.1496 31.7725 32.4092 16 31.6320 32.3096 33.0034 33.7139 34.4416 35.1867 35.9497 36.7311 17 35.3207 36.1366 36.9737 37.8325 38.7135 39.6174 40.5447 41.4961 18 39.3230 40.2986 41.3013 42.3320 43.3913 44.4801 45.5992 46.7494 19 43.6654 44.8247 46.0185 47.2477 48.5135 49.8169 51.1591 52.5412 20 48.3770 49.7469 51.1601 52.6181 54.1222 55.6740 57.2750 58.9267 21 53.4891 55.0997 56.7645 58.4853 60.2638 62.1022 64.0025 65.9667 22 59.0356 60.9210 62.8733 64.8951 66.9889 69.1572 71.4027 73.7283 23 65.0537 67.2516 69.5319 71.8980 74.3529 76.9000 79.5430 82.2854 24 71.5832 74.1361 76.7898 79.5485 82.4164 85.3978 88.4973 91.7197 25 78.6678 81.6230 84.7009 87.9067 91.2459 94.7241 98.3471 102.1210 26 86.3546 89.7650 93.3240 97.0381 100.9143 104.9597 109.1818 113.5884 27 94.6947 98.6194 102.7231 107.0141 111.5012 116.1932 121.0999 126.2312 28 103.7437 108.2486 112.9682 117.9130 123.0938 128.5221 134.2099 140.1699 29 113.5620 118.7204 124.1354 129.8199 135.7877 142.0530 148.6309 155.5373 30 124.2147 130.1084 136.3075 142.8282 149.6875 156.9032 164.4940 172.4799 31 135.7730 142.4929 149.5752 157.0399 164.9078 173.2012 181.9434 191.1590 32 148.3137 155.9610 164.0370 172.5660 181.5741 191.0883 201.1378 211.7529 33 161.9203 170.6076 179.8003 189.5284 199.8236 210.7195 222.2515 234.4575 34 176.6836 186.5358 196.9823 208.0598 219.8068 232.2646 245.4767 259.4894 35 192.7017 203.8577 215.7108 228.3053 241.6885 255.9104 271.0244 287.0871 36 210.0813 222.6952 236.1247 250.4236 265.6489 281.8617 299.1268 317.5135 37 228.9382 243.1810 258.3759 274.5877 291.8855 310.3432 330.0395 351.0586 38 249.3980 265.4594 282.6298 300.9871 320.6147 341.6016 364.0434 388.0421 39 271.5968 289.6871 309.0665 329.8284 352.0731 375.9078 401.4478 428.8165 40 295.6825 316.0347 337.8824 361.3375 386.5200 413.5588 442.5926 473.7702 41 321.8156 344.6877 369.2919 395.7613 424.2394 454.8808 487.8518 523.3316 42 350.1699 375.8479 403.5281 433.3692 465.5421 500.2317 537.6370 577.9731 43 380.9343 409.7346 440.8457 474.4558 510.7686 550.0042 592.4007 638.2153 44 414.3137 446.5864 481.5218 519.3430 560.2917 604.6297 652.6408 704.6324 45 450.5304 486.6627 525.8587 568.3822 614.5194 664.5811 718.9048 777.8572 46 489.8255 530.2456 574.1860 621.9576 673.8987 730.3777 791.7953 858.5876 47 532.4606 577.6421 626.8628 680.4886 738.9191 802.5895 871.9749 947.5928 48 578.7198 629.1858 684.2804 744.4338 810.1164 881.8420 960.1723 1045.7211 49 628.9110 685.2396 746.8656 814.2940 888.0775 968.8216 1057.1896 1153.9075 Uploaded by: Ayman Ayyad (Danger3) 27 Prepared by T: A. JALIL ALAIWI
50 683.3684 746.1981 815.0836 890.6162 973.4448 1064.2817 1163.9085 1273.1830 TABLE No.3 Equation : SN =[(1+ i) N -1] / i SN for one monetary unit N 10.5% 10.75% 11% 11.25% 11.5% 11.75% 12% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.1050 2.1075 2.1100 2.1125 2.1150 2.1175 2.1200 3 3.3260 3.3341 3.3421 3.3502 3.3582 3.3663 3.3744 4 4.6753 4.6925 4.7097 4.7270 4.7444 4.7618 4.7793 5 6.1662 6.1969 6.2278 6.2588 6.2900 6.3214 6.3528 6 7.8136 7.8631 7.9129 7.9630 8.0134 8.0641 8.1152 7 9.6340 9.7084 9.7833 9.8588 9.9349 10.0117 10.0890 8 11.6456 11.7520 11.8594 11.9679 12.0774 12.1880 12.2997 9 13.8684 14.0153 14.1640 14.3143 14.4663 14.6201 14.7757 10 16.3246 16.5220 16.7220 16.9247 17.1300 17.3380 17.5487 11 19.0387 19.2981 19.5614 19.8287 20.0999 20.3752 20.6546 12 22.0377 22.3727 22.7132 23.0594 23.4114 23.7693 24.1331 13 25.3517 25.7777 26.2116 26.6536 27.1037 27.5622 28.0291 14 29.0136 29.5488 30.0949 30.6521 31.2207 31.8007 32.3926 15 33.0600 33.7253 34.4054 35.1005 35.8110 36.5373 37.2797 16 37.5313 38.3508 39.1899 40.0493 40.9293 41.8305 42.7533 17 42.4721 43.4735 44.5008 45.5548 46.6362 47.7455 48.8837 18 47.9317 49.1469 50.3959 51.6798 52.9993 54.3556 55.7497 19 53.9645 55.4302 56.9395 58.4937 60.0942 61.7424 63.4397 20 60.6308 62.3889 64.2028 66.0743 68.0051 69.9972 72.0524 21 67.9970 70.0957 72.2651 74.5076 76.8257 79.2218 81.6987 22 76.1367 78.6310 81.2143 83.8897 86.6606 89.5304 92.5026 23 85.1311 88.0839 91.1479 94.3273 97.6266 101.0502 104.6029 24 95.0699 98.5529 102.1742 105.9392 109.8536 113.9236 118.1552 25 106.0522 110.1473 114.4133 118.8573 123.4868 128.3096 133.3339 26 118.1877 122.9882 127.9988 133.2288 138.6878 144.3860 150.3339 27 131.5974 137.2094 143.0786 149.2170 155.6369 162.3514 169.3740 28 146.4151 152.9594 159.8173 167.0039 174.5351 182.4276 190.6989 29 162.7887 170.4025 178.3972 186.7918 195.6067 204.8629 214.5828 30 180.8815 189.7208 199.0209 208.8059 219.1014 229.9343 241.3327 31 200.8741 211.1158 221.9132 233.2966 245.2981 257.9516 271.2926 32 222.9658 234.8108 247.3236 260.5424 274.5074 289.2609 304.8477 33 247.3772 261.0529 275.5292 290.8535 307.0757 324.2490 342.4294 34 274.3518 290.1161 306.8374 324.5745 343.3895 363.3483 384.5210 35 304.1588 322.3036 341.5896 362.0891 383.8792 407.0417 431.6635 36 337.0955 357.9512 380.1644 403.8241 429.0254 455.8691 484.4631 37 373.4905 397.4310 422.9825 450.2544 479.3633 510.4337 543.5987 38 413.7070 441.1548 470.5106 501.9080 535.4900 571.4097 609.8305 39 458.1462 489.5789 523.2667 559.3726 598.0714 639.5503 684.0102 40 507.2516 543.2087 581.8261 623.3020 667.8496 715.6975 767.0914 41 561.5130 602.6036 646.8269 694.4235 745.6523 800.7920 860.1424 42 621.4719 668.3835 718.9779 773.5462 832.4023 895.8850 964.3595 43 687.7264 741.2347 799.0655 861.5701 929.1286 1002.1515 1081.0826 44 760.9377 821.9175 887.9627 959.4968 1036.9784 1120.9043 1211.8125 45 841.8361 911.2736 986.6386 1068.4401 1157.2309 1253.6106 1358.2300 46 931.2289 1010.2355 1096.1688 1189.6397 1291.3125 1401.9098 1522.2176 47 1030.0080 1119.8358 1217.7474 1324.4741 1440.8134 1567.6342 1705.8838 48 1139.1588 1241.2182 1352.6996 1474.4775 1607.5069 1752.8312 1911.5898 49 1259.7705 1375.6491 1502.4965 1641.3562 1793.3702 1959.7889 2141.9806 50 1393.0464 1524.5314 1668.7712 1827.0087 2000.6078 2191.0641 2400.0182 Uploaded by: Ayman Ayyad (Danger3) 28 Prepared by T: A. JALIL ALAIWI
Uploaded by: Ayman Ayyad (Danger3) 29 Prepared by T: A. JALIL ALAIWI