Question

# You want to make equal deposits at the end of each month for 10 years into...

You want to make equal deposits at the end of each month for 10 years into an account with annual interest rate 8% compounded monthly, and then withdraw \$200 at the end of each month for the following 15 years, ending with a zero balance. How much do your monthly deposits need to be?

#### Homework Answers

Answer #1

For second annuity, monthly withdrawal = \$200 at the end of each month for 15 years

interest rate = 8% compounded monthly.

So, this is an ordinary annuity PV at the year 10 from now is

PV = PMT*(1 - (1+r/n)^(-n*t))/(r/n) = 200*(1 - (1 + 0.08/12)^(-12*15))/(0.08/12) = \$20928.12

Now this value is final value for the 1st annuity for 10 years. So, here PMT is calculated using formula

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) = 20928.12*(0.08/12)/((1+0.08/12)^(12*10) -1) = \$114.40

So, monthly deposits now should be \$114.40

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