Question

Nonannual Compounding

It is now January 1. You plan to make a total of 5 deposits of $500 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 8% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. Do not round intermediate calculations. Round your answers to the nearest cent.

1. How much will be in your account after 10 years?

   $  

2. You must make a payment of $1,984.02 in 10 years. To get the money for this payment, you will make five equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 8% withquarterly compounding. How large must each of the five payments be?

   $  

Answer 1

1: first we need to find the amount accumulated after five deposits

Future Value of annuity due= (1+Rate)*A*((1+rate)^number of periods-1)/rate

= (1+4%)*500*((1+4%)^5-1)/4%

=2816.49

This is the present value after five semiannual periods

We have to find the future value after 16 more semi-annual periods

Future value=Present value*(1+Rate)^number of periods

= 2816.49*(1+4%)^16

=5275.23

2: first we have to find the present value after 8*4 = 32 quarters of the final amount.

Using financial calculator input

FV = 1984.02

I/Y = 8/4=2

N = 32

Solve for PV as -1,052.79

This amount will be the future value after deposits have been made.

Using financial calculator input

FV = 1052.79

I/Y = 2

N = 5

Set BGN=1

Solve for PMT as 198.34

Hence the amount of the five payments= $198.34