Question #230861
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 ?
1
Expert's answer
2021-08-30T16:38:30-0400

It is assumed that, 10.5 years from now.


present value of future withdrawals as on 10.5 years

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


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


monthly payment

=260202.5(150,000×(1+0.5%)66(10,000×(1+0.5%)126))(((1+0.5%)1261)0.5%=\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\%}}


=32,982.12174.9331=\frac{32,982.12}{174.9331}


=$188.5413=\$188.5413 or

=$188.54=\$188.54


Therefore, the monthly payment is $188.54


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