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

The quarterly deposit required is $980.69

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