Question

Grandma decides to put 1500 dollars every month into an account for you. She makes 20 monthly deposits, the last coming September 1, 2003 - the day you start college. She wants you to be able to withdraw money from this account at the beginning of each month, with the first withdrawal coming September 1, 2003 and the last coming June 1, 2008, (when you'll graduate). (Note: that makes 58 withdrawals total.) How much will you be able to withdraw each month if the account is earning a nominal interest rate of 8.1 percent convertible monthly?​

Answer 1

Answer:

551.79 dollars

Step-by-step explanation:

The cash inflows from an annuity paid in arrears (at the end of the period)

The accumulated value (future value ) of a level annuity of amount C  payable in arrears for n periods under interest rate i is given as;

$A=C*\frac{[(1+i)^n-1]}{i}$

In this case;

n=20

C=1500

$i^{(12)}=8.1%$

We have to convert this nominal rate of interest p.a to effective interest rate per month as follows;

$i=\frac{i^{(12)}}{12}\\ i=\frac{8.1}{12}\\ i=0.675%$

then

$A=C*\frac{(1+i)^n-1}{i}\\ A=1500*\frac{(1+0.00675)^{20}-1}{0.00675} \\\\A=1500*21.33596405\\\\A=32003.94608$

Therefore the accumulated amount is 32003.95 dollars

If the student makes 58 withdrawals, then the amount that is withdrawn every month is

$\frac{32003.94608}{58} =551.7921737$

551.79 dollars