Answer to Question #229390 in Financial Math for Vhhgf

Question

Michael is updating his estate plan for himself and his family. He would like to provide an income of $ 3000 every month starting 101 2 years from now and continuing for the next 20 years. He has started his account with an initial deposit of $ 10,000 and he knows his life insurance, maturing in five years, will have a cash value of $ 150,000. To make up the difference , Michael has decided to make monthly deposits in the account. How much should each deposit be if all interest is computed at 6 percent compounded monthly ?

Answer 1

It is assumed that, 10.5 years from now.

present value of future withdrawals as on 10.5 years compounded monthly

period(12 months)= 10.5*12=126

Present value of future withdrawal as at 10. 5 years=3000 x ((1-(1 + 0.5%)¹¹⁴)/0.5%)

=3000/86.73416

=$260202.5

Monthly payment= (amount required at 10.5 years-future value of 150000-future value of 10000) /future value annuity (126.5%)

= (260202.5-150000*(1 + 0.5%)⁶⁶ -10000*(1+0.5%)¹²⁶) / (((1 + 0.5%)¹²⁶-1) / 0.5%)

= 32982.12 / 174.9331

=$ 188.54

Monthly payment is $ 188.54