Question

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?

Answer 1

Deposit= $94.19

Step-by-step 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