Answer to Question #230861 in Financial Math for Hiyuiiu

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

$=3,000\times(\frac{1-(1+0.5\%)^{-114})}{0.5\%})$

$=3,000\times 86.73416\\=\$260,202.5$

monthly payment

$=\frac{260202.5-(150,000\times(1+0.5\%)^{66}-(10,000\times(1+0.5\%)^{126}))}{(\frac{((1+0.5\%)^{126}-1)}{0.5\%}}$

$=\frac{32,982.12}{174.9331}$

$=\$188.5413$ or

$=\$188.54$

Therefore, the monthly payment is $188.54