Question

You believe you will need to have saved $500,000 by the time you retire in 47 years in order to live comfortably. You also believe that you will inherit $10,000 in 10 years. If the interest rate is 9% per year, how much must you save each year to meet your retirement goal?

Answer 1

>>>>

Let P = annual deposit

r = interest rate = 9%

n = 47 years

Future value of annual deposits = P[(1+r)^n - 1] /r

= P [(1+9%)^47 - 1] / 9%

= P * 56.4176486209 / 0.09

= P * 626.862762454

>>>>

Future value of $10,000 to be received in 10 years at 47 years from now = $10,000 * (1+9%)^37

= $10,000 * 24.253835284

= $242,538.35284

>>>>

Future value of $10000 received in 10 years and annual deposits should equal $500,000

$242,538.35284 + P * 626.862762454 = $500,000

P * 626.862762454 = $257,461.64216

P = $410.714526

Therefore, Annual Deposit amount is $410.71