This project contains questions from Chapter 10 project page 522 Exercises Solut

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This project contains questions from Chapter 10 project page 522 Exercises Solutions Hints 1. Suppose a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the two-year period? Find the interest earned after the 1st year 1.03x100,000= ANS_____________________ $103,000 Investment grows from present value P to a future value F = P + I by adding an interest amount I. Interest amount is earned on the Find the interest earned in the 2nd year (on current balance) current balance I = B*i*n 1.04x103,000 Current balance is the future value. ANS_____________________ $107,120 Find the interest earned after the two years Year 1 1.03+100000=103000 f = (1+ i)-P Year 2 1.04+103000=107120 107120 = (1+i)-100000 ANS_____________________ 7.12% 107120/100000-1 = i 0.0712 = i Find the interest rate at which the original investment would earn the interest after the 2nd year. ANS_____________________ 2. Rework Exercise 1 for the case where the investment earns 4% during the first year and 3% during the second year. Is the answer to Ex 2 greater, less than, or equal to the answer to Ex 1. (show calculation here) ANS______________________________________ 3. Consider an annuity in which $100000 is invested and $10000 is withdrawn at the end of each year. Suppose the interest rate is 3% during the first year and 4% during the second year. What is the balance at the end of the second year? Find the interest after the first year Work out year 1 first. Find the current balance for the year 2. Work out year 2. Use still formulas of Ex 1 F=P+I and I=B*i*n ANS__________________ Find the current balance after year 1 ANS__________________ Find the interest earned in the second year ANS__________________________ Find the balance after the second year ANS__________________________ 4.Rework Ex3 where the interest rate is 4% during the first year and 3% during the second year. Is the balance at the end of the second year greater than, less than, or equal to the answer to Ex 3? (show calculation here) ANS______________________________________________ 5.(this is Exercise 8 page 522) Which of the following statements is true? a) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. Find interest after year1 Work out year one and year two. When investment loses value F=P-I. Use any value for P ANS__________________ Find current balance after year one ANS___________________ Find interest after year two ANS____________________ Find current balance or value of the investment after year two ANS_______________________ ANS_____________________TRUE            OR               FALSE b) Suppose investment A earns 4% one year and then loses 3% the next year, and investment B loses 3% one year and then gains 4% the next year. Then the balances of the two investments will be the same after the two-year period. for investments A B Find interest after year1 Use $1000 for the principal of both investments. ANS__________________ Find current balance after year one ANS___________________ Find interest after year two ANS____________________ Find current balance or value of the investment after year two ANS_______________________ ANS_____________________TRUE            OR               FALSE 6. (Exercise 9 page 522) Show that if $1000 is invested at 8% compounded annually, then it will double in about 9 years. (Note: 9= 72/8, the rule of 72) years F Calculate and determine in which year 1 the investment is doubled. 2 3 4 5 6 7 8 9 10 11 7. (Exercise 10) Show that if $1000 is invested for 6 years, then it will approximately double in that time if it appreciates at 12% per year compounded annually.( Note 12=72/6) interest rate F 1 Calculate and determine at which interest rate 2 the investment is doubled. 3 4 5 6 7 8 9 10 11 12 13 14 This project contains questions from Chapter 10 project page 522 Exercises Solutions Hints 1. Suppose a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the two-year period? Find the interest earned after the 1st year 1.03x100,000= ANS_____________________ $103,000 Investment grows from present value P to a future value F = P + I by adding an interest amount I. Interest amount is earned on the Find the interest earned in the 2nd year (on current balance) current balance I = B*i*n 1.04x103,000 Current balance is the future value. ANS_____________________ $107,120 Find the interest earned after the two years Year 1 1.03+100000=103000 f = (1+ i)-P Year 2 1.04+103000=107120 107120 = (1+i)-100000 ANS_____________________ 7.12% 107120/100000-1 = i 0.0712 = i Find the interest rate at which the original investment would earn the interest after the 2nd year. ANS_____________________ 2. Rework Exercise 1 for the case where the investment earns 4% during the first year and 3% during the second year. Is the answer to Ex 2 greater, less than, or equal to the answer to Ex 1. (show calculation here) ANS______________________________________ 3. Consider an annuity in which $100000 is invested and $10000 is withdrawn at the end of each year. Suppose the interest rate is 3% during the first year and 4% during the second year. What is the balance at the end of the second year? Find the interest after the first year Work out year 1 first. Find the current balance for the year 2. Work out year 2. Use still formulas of Ex 1 F=P+I and I=B*i*n ANS__________________ Find the current balance after year 1 ANS__________________ Find the interest earned in the second year ANS__________________________ Find the balance after the second year ANS__________________________ 4.Rework Ex3 where the interest rate is 4% during the first year and 3% during the second year. Is the balance at the end of the second year greater than, less than, or equal to the answer to Ex 3? (show calculation here) ANS______________________________________________ 5.(this is Exercise 8 page 522) Which of the following statements is true? a) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. Find interest after year1 Work out year one and year two. When investment loses value F=P-I. Use any value for P ANS__________________ Find current balance after year one ANS___________________ Find interest after year two ANS____________________ Find current balance or value of the investment after year two ANS_______________________ ANS_____________________TRUE            OR               FALSE b) Suppose investment A earns 4% one year and then loses 3% the next year, and investment B loses 3% one year and then gains 4% the next year. Then the balances of the two investments will be the same after the two-year period. for investments A B Find interest after year1 Use $1000 for the principal of both investments. ANS__________________ Find current balance after year one ANS___________________ Find interest after year two ANS____________________ Find current balance or value of the investment after year two ANS_______________________ ANS_____________________TRUE            OR               FALSE 6. (Exercise 9 page 522) Show that if $1000 is invested at 8% compounded annually, then it will double in about 9 years. (Note: 9= 72/8, the rule of 72) years F Calculate and determine in which year 1 the investment is doubled. 2 3 4 5 6 7 8 9 10 11 7. (Exercise 10) Show that if $1000 is invested for 6 years, then it will approximately double in that time if it appreciates at 12% per year compounded annually.( Note 12=72/6) interest rate F 1 Calculate and determine at which interest rate 2 the investment is doubled. 3 4 5 6 7 8 9 10 11 12 13 14

Explanation / Answer

1. Using the Formula A = P + PNR/100 So For the !st Year A = 100000 + 100 000 * 1*3/100 =1,0 3,000.

So During the Second Year A1 = 1,03,000 + 1,03,000 * 4/100 = 1,07,120.

2. With Changed Interest Rates A = 100000 + 100000*4/100 = 1,04,000.

So During the Second year A1 = 1,04,000 + 1,04,000 * 3/100 = 1,071,20

Both Amounts are same

3. A is False, Because the Value wont be the Same. Increase by 4 % means A = P.*1.04

And Reduction by 4% means P*1.04 -(P*1.04)(0.04) Which is not P.

4. Lets Take P =1000 For Intvestement A Earn 4% i.e 1040 and Lose 3% i,e 1040 - 31.2 = 1008.8

For Investment B Earn 3% i,e 1030 and then Lose 4% i.e 1030 - 41.2 = 998.8.

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