Question

Please don't use excel to solve the problems and show your work.

16.1. (a) Calculate the amount realized at the end of 7 years through annual deposits of $1000 at 10 percent compound interest. (b) What would the amount be if interest were compounded semiannually? 16.2. A young woman purchases a used car. After down payment and allowances, the amount to be paid is $8000. If money is available at 10 percent, what is the monthly payment to pay off the loan in 4 years? What would it be at 4 percent interest?

Answer 1

Answer to Question 16.1:

Part (a):

Annual deposit = $1,000
Number of deposits = 7
Interest rate = 10%

Future value = $1,000*1.10^6 + $1,000*1.10^5 + … + $1,000*1.10 + $1,000
Future value = $1,000 * (1.10^7 - 1) / 0.10
Future value = $1,000 * 9.48717
Future value = $9,487.17

Part (b):

Annual deposit = $1,000
Number of deposits = 7

Annual interest rate = 10%
Semiannual interest rate = 5%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.05)^2 - 1
Effective annual rate = 1.1025 - 1
Effective annual rate = 0.1025 or 10.25%

Future value = $1,000*1.1025^6 + $1,000*1.1025^5 + … + $1,000*1.1025 + $1,000
Future value = $1,000 * (1.1025^7 - 1) / 0.1025
Future value = $1,000 * 9.56031
Future value = $9,560.31