Financial mathematics 111 Chapter four: Annuities

Transcription

1 Financial mathematics 111 Chapter four: Annuities Bank اسم الطالب:... رقم الطالب:... الصف:... المدرسة:... الرقم التسلسلي

2 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 st year 1 2 nd year 2 3 rd year 3 4 th year 4 CA=100(1+0.07) 3 = BD CA=100(1+0.07) 2 = BD CA=100(1+0.07) 1 = BD CA=100(1+0.07) = BD Total Sn = BD 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 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 CA=100(1+0.07) 3 = BD CA=100(1+0.07) 2 = BD CA=100(1+0.07) = BD Total Sn = BD Prepared by T: A. JALIL ALAIWI 1

3 **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

4 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

5 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

6 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

7 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

8 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

9 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 BD what is the value of each ordinary annuity? Exercise 13: What quarterly deposit will accumulate to BD in five years at 12 % annually compounded quarterly? Uploaded by: Ayman Ayyad (Danger3) 9 Prepared by T: A. JALIL ALAIWI

10 Exercise 14: Sajeda deposits a sum of money at the beginning of each year at 4% annually and the amount of annuity became BD 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 BD 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 Find the value of each annuity? Uploaded by: Ayman Ayyad (Danger3) 10 Prepared by T: A. JALIL ALAIWI

11 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 $ 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 BD Find the value of each annuity? Exercise 19: What semi annually payment will accumulate to BD in five years at 8% annually compounded semi- annually? Uploaded by: Ayman Ayyad (Danger3) 11 Prepared by T: A. JALIL ALAIWI

12 Exercise 20: Bilal paid an annuity every year at 6% annually if the amount of annuities after 10 years was BD Find the value of each annuity? Uploaded by: Ayman Ayyad (Danger3) 12 Prepared by T: A. JALIL ALAIWI

13 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, 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 BD 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 Find the rate of the compound interest? Uploaded by: Ayman Ayyad (Danger3) 13 Prepared by T: A. JALIL ALAIWI

14 Exercise 24: Omran pays at the end of each year BD200. If the total compound interest at the end of 4 years BD 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 Find the compound interest rate? Uploaded by: Ayman Ayyad (Danger3) 14 Prepared by T: A. JALIL ALAIWI

15 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, ? Exercise 27: Shehab deposited at the beginning of every 3 months BD500. If the total amount after 3 years became BD7, find the compound interest rate and the total compound interest?. Uploaded by: Ayman Ayyad (Danger3) 15 Prepared by T: A. JALIL ALAIWI

16 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 BD Find the compound interest rate? Uploaded by: Ayman Ayyad (Danger3) 16 Prepared by T: A. JALIL ALAIWI

17 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, 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 BD at 5% annually? Uploaded by: Ayman Ayyad (Danger3) 17 Prepared by T: A. JALIL ALAIWI

18 Exercise 31 Yousif deposits BD340 at the end of each 4 months at 9% annually. He earns total amount annuities of B 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 BD ? Exercise 33: How long will it take for BD 45 deposited at the end of each 4 months to be BD at the rate of 2.5% every 4 months? Uploaded by: Ayman Ayyad (Danger3) 18 Prepared by T: A. JALIL ALAIWI

19 .. Exercise 34: How long would it take BD50 deposited at the beginning of each semi- annually to become to BD at 10 % annually? Exercise 35: How long will take BD120 deposits at the beginning of every year to amount BD at 4% annual rate? Uploaded by: Ayman Ayyad (Danger3) 19 Prepared by T: A. JALIL ALAIWI

20 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 BD , find the: A- Number of payments B- Time of annuities C- Compound interest. Exercise 37 Nasser wishes to borrow BD 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

21 Uploaded by: Ayman Ayyad (Danger3) 21 Prepared by T: A. JALIL ALAIWI

22 1. Find the value of the following: A- 15 6% B % 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 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 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, ? 4. Sameera deposited BD600 in a bank at the end of every 6 months for 10 years if the fund accumulated for her was BD 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, Find the compound interest rate? 6. A man pays BD70 at the end of each year. His total amount after 15 years was BD 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 BD ? 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

23 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% Uploaded by: Ayman Ayyad (Danger3) 23 Prepared by T: A. JALIL ALAIWI

24 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% Uploaded by: Ayman Ayyad (Danger3) 24 Prepared by T: A. JALIL ALAIWI

25 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% Uploaded by: Ayman Ayyad (Danger3) 25 Prepared by T: A. JALIL ALAIWI

26 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% Uploaded by: Ayman Ayyad (Danger3) 26 Prepared by T: A. JALIL ALAIWI

27 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% Uploaded by: Ayman Ayyad (Danger3) 27 Prepared by T: A. JALIL ALAIWI

28 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% Uploaded by: Ayman Ayyad (Danger3) 28 Prepared by T: A. JALIL ALAIWI

29 Uploaded by: Ayman Ayyad (Danger3) 29 Prepared by T: A. JALIL ALAIWI