Question

Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into a retirement savings account that will earn 12% compounded monthly. Then one year after making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12% compounded monthly. How much should the monthly deposits be for his retirement plan?

Answer 1

Solution :-

Value of Money of Deposits at the time of Retirement = Deposit * FVAF ( r , n )

Monthly Deposit be X

Rate per month = 12% / 12 = 1%

Total Deposits = 34 * 12 = 408

Now Value at Retirement = X * FVAF ( 1% , 408 )

= X * 5695.895

Now the Present Value of Annual Withdrawal at the time of Retirement = $100,000 * PVAF (  r , n )

r = Annual Rate = ( 1 + 0.12 / 12 )¹² - 1 = 0.1268 = 12.68%

Total Annual Withdrawal = 25

= $100,000 * PVAF ( 12.68% , 25 )

= $100,000 * 7.4877

= $748,767.698

Now the Value of money for nephew = $1,000,000 * PVF ( 12.68% , 25 )

= $1,000,000 * 0.050535

= $50,534.52

Now as per question =

= X * 5695.895 = $748,767.698 + $50,534.52 = $799,302.20

X = $133.531

Deposit per month = $133.531

If there is any doubt please ask in comments