Question

A woman is planning to retire in 30 years. She wishes to deposit a regular amount every three months until she retires, so that beginning one year after retirement she will receive annual payments of $40,000 for the next 20 years. How much must be deposited every three months if the interest rate is 8%, compounded quarterly

Answer 1

The quarterly deposit required is $980.69

Step-by-step explanation:

Giving the following information:

I will assume that the retirement age is 65 years.

First, we need to calculate the future value required one year after retirement.

FV= 40,000*20= $800,000

Number of years= 66 - 30= 36 years*4= 144

Interest rate= 0.08/4= 0.02

Now, to calculate the quarterly deposit required, we need to use the following formula:

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

A= quarterly deposit

Isolating A:

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

A= (800,000*0.02) / [(1.02^144)-1]

A= $980.69