Financial mathematics 111 Chapter two: Compound Interest

Transcription

1 Financial mathematics 111 Chapter two: Compound Interest Bank اسم الطالب:... رقم الطالب:... الصف:... المدرسة:... الرقم التسلسلي

2 Compound interest:.. KEY TERM INTRODUCED: Compound amount:.. Unit four and five: calculate compound amount and compound interest. Example: A person invested BD 1000 in a bank for 3 years at 7% annually. Find the simple interest and compound amount at the end of each year.-- No of year Simple Interest SI = P x i x T Compound Interest CI = P x i x T 1 SI = % 1 = BD 70 2 SI = % 1 = BD 70 CI = % 1 = BD 70 CA = = BD 1070 CI = % 1 = BD 75 CA = = BD SI = % 1 = BD 70 CI = % 1 = BD 80 CA = = BD 1225 Notices Total SI =.. A=. Total CI =.. A=.. P =. I =. N (T)=... CA =. CI=.. CA = P x (1 + i ) N CI = P x (1 + i ) N - 1. Uploaded by: Ayman Ayyad (Danger3) 2 Prepared by T: A. JALIL ALAIWI

3 Exercise 2-1: Find the value of the following (by using calculator and the interest table):- Calculator interest table a -(1.06) 12 = b-(1.05) 60 = c -(1.005) 125 = Exercise 2-2: Rabab deposited BD4,200 for 14 years at 5.6% annually. Find the compound interest at the end of the period?..... Exercise 2-3: A trader wants to borrow 20,000 and pays it after 3 years, he has two choices: Borrowing on a simple interest at 5¾% annually Borrowing on a compound interest at 4% annually Which choice he should choose (by knowing the interest)? Why?..... He should choose interest, because it interest. Uploaded by: Ayman Ayyad (Danger3) 3 Prepared by T: A. JALIL ALAIWI

4 Exercise 2-4: Find the compound amount of BD1 at 12% annually for 8 years without using tables?. Exercise 2-5: Find the compound amount and compound interest for BD1 at 4.5% annually for 74 years by using interest tables?. Exercise 2-6: A person deposited $6000 for 4 years at 5.5% annually. Find the compound amount and the compound interest at the end of the period?. Uploaded by: Ayman Ayyad (Danger3) 4 Prepared by T: A. JALIL ALAIWI

5 Unit six: Annual and partial interest rate:.. Note: Must achieve compatibility between the arithmetic interest rate and the number of times the ramp. ملاحظة: یجب تحقیق التطابق الحسابي بین معدل الفاي دة وعدد مرات التعلیة. One year = month. Example: Suppose 12% annually for 5 years compounding for the following Type of compounding: 1-Monthly: (Twelfth times a year / every month) n =.. i =.. ( ) 2-Semi-annually: (Two times a year / every 6 months) Annually: n = 5 i = 12% ( ) 5 One time a year n =.. i =.. ( ) 3- Thirdly: (Three times a year / every 4 months) n =.. i =.. ( ) 4-Quarterly: (Four times a year / Every 3 months) n =.. i =.. ( ) Uploaded by: Ayman Ayyad (Danger3) 5 Prepared by T: A. JALIL ALAIWI

6 Exercise 2-7 Suppose 24% annually for 10 years compounding for the following Type of compounding: 1-Monthly: (Twelfth times a year / every month) n =.. i =.. ( ) 2-Semi-annually: (Two times a year / every 6 months) Annually: n = 10 i = 24% (1. 24 ) 10 One time a year n =.. i =.. ( ) 3- Thirdly: (Three times a year / every 4 months) n =.. i =.. ( ) 4-Quarterly: (Four times a year / Every 3 months) n =.. i =.. ( ) Uploaded by: Ayman Ayyad (Danger3) 6 Prepared by T: A. JALIL ALAIWI

7 Exercise 2-8: Shahd invested BD1000 in a bank at 6% annually for 4 years find the compound amount if the interest is: 1- Compounded annually 2- Compounded semi-annually. 3-Compounded thirdly 4-Compounded quarterly.. 5-Compounded monthly... Uploaded by: Ayman Ayyad (Danger3) 7 Prepared by T: A. JALIL ALAIWI

8 Uploaded by: Ayman Ayyad (Danger3) 8 Prepared by T: A. JALIL ALAIWI

9 Exercise 2-9: A woman deposited BD5,000 in a bank that pays 7.8% annually compounded quarterly on saving accounts for 4years and 6 months. Find the compound amount.. Exercise 2-10: Ali deposited BD3000 at 4% every 4 months find the compound amount at the end of 8 years and 8 months?. Exercise 2-11: Mariam deposited BD2550 in a bank at an effective rate of 6%annually. If the interest compounded semi-annually Calculate her fund at the end of 8 years, then find the compound interest?.. Uploaded by: Ayman Ayyad (Danger3) 9 Prepared by T: A. JALIL ALAIWI

10 Exercise 2-12: Faisal wants to borrow KD7200 from a bank to buy a new car if you know the interest rate is 6% annually compounded monthly. Find how much he paid to the bank at the end of 10 years?. Exercise 2-13: Sakeena Ahmed deposited BD2600 in a bank at 12% annually compounded quarterly- Find her fund at the end of 5 years and 9 months? And find the compound interest?. Exercise 2-14: A person deposited BD8750 at 3% each quarter find the amount and the interest at the end of 6 years?. Uploaded by: Ayman Ayyad (Danger3) 10 Prepared by T: A. JALIL ALAIWI

11 Exercise 2-15: A person deposited BD3500 at 4% every 6 months. Find the amount at the end of 8 years and 6 months?. Exercise 2-16: Laila borrowed $6400 from a bank at 5% every 4 months. Find the amount she paid at the end of three years and 8 months? And calculate the interest?. Uploaded by: Ayman Ayyad (Danger3) 11 Prepared by T: A. JALIL ALAIWI

12 Changeable interest rate: Exercise 2-17: Hashim invested BD5,000 for 6 years at 4% annually for the first two years, 6% annually for the following 3 years and 7% annually for the last year find the compound interest at the end of the period? Calculate the interest? Interest rate: 4% 6% 7% Years: years 3years 1year. Exercise 2-18: Find the compound interest for BD10,000 invested for 4 years, if you know that the rate is changing as follows : 3% for the first year, 2.5% for the second year, 2% for the third year and 1% for the fourth year?.. Uploaded by: Ayman Ayyad (Danger3) 12 Prepared by T: A. JALIL ALAIWI

13 Exercise 2-19: What is the compound amount for BD2,000 invested at 6% for 3 years and 4.8% for 5 more years?... Exercise 2-20: Find the total amount that saad will get if he saves BD2,000 in a bank for 10 years at changing rate, as following: at 5% annually for the first 5 years, 4.6% annually for the sixth year and 5.25 % annually for the rest years?. Exercise 2-21: Find the compound amount for BD2,000 invested for 7 years at 4.5% for the first 3 years and 5¾% for the rest years?. Uploaded by: Ayman Ayyad (Danger3) 13 Prepared by T: A. JALIL ALAIWI

14 ..... Changeable principal:... P=1,000 CA=1,500 P CA Exercise 2-22: Fayez invested BD3500 at 7% annually after 3 years he withdrew from his account BD1000 and invested the rest at 8% annually - find the compound amount and the interest at the end of 10 years?.. Uploaded by: Ayman Ayyad (Danger3) 14 Prepared by T: A. JALIL ALAIWI

15 Exercise 2-23: Noora invested BD4000 at Al- Ahli bank at interest rate of 9% annually and after 3 years she deposited BD3000 to her account at 4% every 4 months find the compound amount and the compound interest at the end of 8 years from the first deposit?. Exercise 2-24: A person deposited BD7,000 at 6% annually, after two years he withdrew BD2,618 from his account and invested the rest at 7.5% annually. Find: a- His fund after withdrawal b- The compound amount for the remaining sum at the end of four years.. Uploaded by: Ayman Ayyad (Danger3) 15 Prepared by T: A. JALIL ALAIWI

16 Exercise 2-25: Dawood deposited BD3,000 at a compound interest of 8% annually, after 3 years he added BD to his account and the rate of interest increased to 10% annually. Find the amount at the end of 8 years from the first deposit.. Exercise 2-26: A trader borrowed BD20,000 on 1 st January 2000 from BBK and BD15,000 on 1 st January 2001 and finally BD30,000 on 1 st January He promised to pay the debt on 31/12/ If the bank gives compound interest rate of 12% annually find the amount that should be paid on 31/12/ Uploaded by: Ayman Ayyad (Danger3) 16 Prepared by T: A. JALIL ALAIWI

17 Finding the principal: First: Finding the Principal by knowing amount: CA = P x (1 + i ) N Exercise 2-27: Hassan deposited an amount of money in a bank at 5% annually. If the compound amount at the end of 12 years is BD8, Calculate the principal? Exercise 2-28: Find the principal if the compound amount after 5 years is BD and the compound interest rate is 8% annually, then find the interest? Uploaded by: Ayman Ayyad (Danger3) 17 Prepared by T: A. JALIL ALAIWI

18 Exercise 2-29: Find the principal if the compound amount at the end of 7 years is BD6,450 and the compound interest rate is 4.5% annually for the first three years and 5% annually for the rest years? Exercise 2-30: How much must be deposited for an investment paying 8% annually compounded quarterly to give an amount of BD2, in 5 years? Uploaded by: Ayman Ayyad (Danger3) 18 Prepared by T: A. JALIL ALAIWI

19 Exercise 2-31: A man deposited money in NBB at 3%annually, after 5 years he withdrew BD from his account and invested the rest for 5 years at 2% every 6 months if the amount at the end of the period is BD3657 find the principal? Uploaded by: Ayman Ayyad (Danger3) 19 Prepared by T: A. JALIL ALAIWI

20 Second: Finding the Principal by knowing the interest:. CI = P x (1 + i ) N Exercise 2-32: A person deposited an amount of money in a bank at 3% annually. If the compound interest at the end of 10 years was BD find: a) The deposited amount? b) The compound amount at the end of the period Exercise 2-33: Find the principal that generates an interest of BD700 at 2% annually for 5 years? Uploaded by: Ayman Ayyad (Danger3) 20 Prepared by T: A. JALIL ALAIWI

21 Exercise 2-34: Taha calculated the compound interest he will get if he deposits his money in a bank at 3% annually for 20 years and it was BD , find the principal? Exercise 2-35: A principal invested for 3 years and a half at 5.75% every 3 months which gives an interest of BD Find the compound amount? Uploaded by: Ayman Ayyad (Danger3) 21 Prepared by T: A. JALIL ALAIWI

22 Finding the Time/periods:.. CA = P x (1 + i ) N... Exercise 2-36: A principal of BD invested at 8% annually, how long would it take to make the amount to BD ? A. By using calculator B. By using interest table No 1: page Searching for under 8%. Press log.. log. N 8% 8.25% 8.5% 8.75% We find n = 23 years. Exercise 2-37: How long will it take for BD1600 at 4% every semi-annual to make the amount to BD ? Uploaded by: Ayman Ayyad (Danger3) 22 Prepared by T: A. JALIL ALAIWI

23 Exercise 2-38: A loan of BD2,000 amounted to BD Find interest rate was 5% annually? the borrowing period if the Exercise 2-39: Nawal borrowed BD5,000 from a bank at 6% annually Find the borrowing period if the compound interest was BD8954? Exercise 2-40: How long will it take BD2,000 at 2.5% compounded every semi-annually to give an interest of BD ? Uploaded by: Ayman Ayyad (Danger3) 23 Prepared by T: A. JALIL ALAIWI

24 Exercise 2-41: How long will it take an investment of BD4,000 to amount of BD 5, at 7% annually? Exercise 2-42: How long will it take the money to double itself at 4% annually? Exercise 2-43: How long will it take the money to triple itself at 6.5% annually? Uploaded by: Ayman Ayyad (Danger3) 24 Prepared by T: A. JALIL ALAIWI

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

26 Finding the interest rate:. CA = P x (1 + i ) N.. Exercise 2-44: Mahmood deposited BD3000 in the bank, if the amount at the end of 6 years was BD Find the interest rate? A. By using calculator B. By using interest table No 1: page Press x = Searching for opposite to n=6 b) By using interest table No 1 Searching for opposite to n = 6. N 8.75% 8.5% 9% 9.25% We Find the i = 9% Exercise 2-45: Saad deposited BD1400 in a bank that gives compound interest of BD at the end of 10 years - Find the rate of interest? Uploaded by: Ayman Ayyad (Danger3) 26 Prepared by T: A. JALIL ALAIWI

27 Exercise 2-46: Tahera borrowed 4,500 from a bank that gives compound interest of 1,916 at the end of 3 years. Find the quarterly interest rate and the annual rate of interest? Exercise 2-47: If BD 6,600 amounts to BD10, in 10 years. Find the rate of interest? Exercise 2-48: Jawad borrowed BD8,000 for 4 years. If the compound interest was BD2, find the semi-annually interest rate, and the annually interest rate? Uploaded by: Ayman Ayyad (Danger3) 27 Prepared by T: A. JALIL ALAIWI

28 Exercise 2-49: Find the rate of interest for amounts to 10,000 after 13 years? Uploaded by: Ayman Ayyad (Danger3) 28 Prepared by T: A. JALIL ALAIWI

29 General Exercise 1. Find the compound amount & interest of BD 2500 at the end of 20 years at 5.25% annually. 2. Find the compound interest and compound amount for BD 1500 invested at 6.25% annually for 25 years. 3. Find the compound amount for BD8, 750 invested for 10 years, if you know that the rate is changing as follows: 5% for the first 5 years, 5.25% for the sixth year, 5.5% for the rest years? 4. Ahmed invested BD 7,400 at 6.5% annually; find the compound amount after 85 years? 5. Moayyed deposited BD1400 at 6% annually, find the compound amount at the end of 10 years and 8 months if you know that interest is compounded quarterly. 6. Shahd invested BD 6000 at 10% annually compounded semi- annually find the compound amount at the end of 4 years and 5 months? 7. Malak invested BD 3150 at 2¼% every semi annual, find the compound amount at the end of 4 years and 7 months? 8. Omar borrowed BD 6,000 from BBK for 5 years at 4% annually compounded semi - annually. Two years from the borrowing date he borrowed BD 2, at 2% annually compounded quarterly. 9. How much would he pay after 7 years from first borrowed date? 10. Fawaz wants to buy a new house at Sanad, he has two choices either to pay BD65,000 cash today or to pay BD73,500 after 3 years. If you know that, the compound interest rate at market is 7% annually. Which choice is better for him if he wants to make a decision? Why? 11. Jassim deposited money in B.B.K for investment at 5%annually, after 5 years he added BD to his account at a new interest rate of 5.5% annually. After another 3 years, his account was BD Find the first sum deposited? Uploaded by: Ayman Ayyad (Danger3) 29 Prepared by T: A. JALIL ALAIWI

30 TABLE No.1 Equation : CA = P ( 1 + i ) N CA for one monetary unit N 0.5% 0.75% 1% 1.25% 1.5% 1.75% 2% 2.25% 2.5% Uploaded by: Ayman Ayyad (Danger3) 30 Prepared by T: A. JALIL ALAIWI

31 TABLE No.1 Equation : CA = P ( 1 + i ) N CA for one monetary unit N 2.75% 3% 3.25% 3.5% 3.75% 4% 4.25% 4.5% 4.75% Uploaded by: Ayman Ayyad (Danger3) 31 Prepared by T: A. JALIL ALAIWI

32 TABLE No.1 Equation : CA = P ( 1 + i ) N CA for one monetary unit N 5% 5.25% 5.5% 5.75% 6% 6.25% 6.5% 6.75% 7% Uploaded by: Ayman Ayyad (Danger3) 32 Prepared by T: A. JALIL ALAIWI

33 TABLE No.1 Equation : CA = P ( 1 + i ) N CA for one monetary unit N 7.25% 7.5% 7.75% 8% 8.25% 8.5% 8.75% 9% 9.25% Uploaded by: Ayman Ayyad (Danger3) 33 Prepared by T: A. JALIL ALAIWI

34 TABLE No.1 Equation : CA = P ( 1 + i ) N CA for one monetary unit N 9.5% 9.75% 10% 10.25% 10.5% 10.75% 11% 11.25% 11.5% Uploaded by: Ayman Ayyad (Danger3) 34 Prepared by T: A. JALIL ALAIWI

35 Uploaded by: Ayman Ayyad (Danger3) 35 Prepared by T: A. JALIL ALAIWI