Question

A savings plan requires you to make payments of $250 each at the end of every month for a
year. The bank will then make six equal monthly payments to you, with its first payment due
one month after the last payment you make to the bank. Compute the size of each monthly
payment made by the bank, assuming a nominal interest rate of 4% p.a. payable monthly

Answer 1

solution

The interest rate, $4\%$ p.a hence the monthly compounding rate (r) is:

$$r=\frac{4\%}{12}$$

The savings:

$Payment,p=250$

$Number \ of \ payments,n=12$

The value of the payments at the end of 1 year

$$FV=p*\frac{ (1+r)^n-1}{r}$$

$$=250*\frac{ (1+ \frac{0.04}{12} )^{12}-1}{\frac{0.04}{12}}=3055.6157$$

Withdrawal:

At the end of the savings period, The present value of withdrawal amounts should be equal to the accumulated value of savings:

$$PV=p*\frac{ 1-(1+r)^{-n}}{r}$$

$$3055.6157=p*\frac{ 1-(1+ \frac{0.04}{12})^{-6}}{ \frac{0.04}{12}}$$ $$3055.6157= p* 5.9306$$

$$p=\frac{3055.6157}{5.9306} =515.2272$$

answer: the bank pays $515.23 at the end of every month for 6 months