You must make a payment of $1,432.02 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 12% with quarterly compounding. How large must each of the five payments be?

Deposit = $94.19

Explanation:

Giving the following information:

You must make a payment of $1,432.02 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 12% with quarterly compounding.

First, we need to calculate the present value one year from today of $1,432.02.

We need to use the following formula:

PV = FV / (1+i) ^n

n = 9*4 = 36

i = 0.12/4 = 0.03

PV = 1,432.02 / 1.03^36 = 494.09

This is the monetary value we need to generate one year from today to achieve $1,432.02 ten years from now.

We will use the following formula:

FV = {A*[ (1+i) ^n-1]}/i

A = annual deposit

Isolating A:

A = (FV*i) / {[ (1+i) ^n]-1}

i = 0.12/5 = 0.024

A = (494.09*0.024) / [ (1.024^5) - 1]

A = $94.19