Question

HW21: Problem 4 Previous Problem Problem List Next Problem (1 point) Grandma decides to put 1100 dollars every month into an account for you. She makes 18 monthly deposits, the last coming September 1, 2019 - 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, 2019 and the last coming June 1, 2024, (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 7.5 percent convertible monthly? Answer dollars.

Answer 1

First we have to calculate the future value of annuity to find out the balance in account as on September 1, 2019 after last deposit.

Future value of annuity = P *[ ((1 + r)^n - 1)/ r ]
Here P = Annuity amount
r = interest rate = 7.5% /12 = 0.625%
n = no. of payments = 18

Future value = $1100 *[ ((1 + 0.00625)^18 - 1)/ 0.00625 ]
Future value = $1100 * 18.9889 = $20,887.80

Hence this will be the balance in account as on September 1, 2019 after last deposit.

Now for finding the monthly withdrawl amount we have to use the present value annuity due formula and find the annuity amount.
Present value of annuity due = P + P * [ (1 - (1+r)^-(n-1)) / r ]
Here P = Annuity amount
r = interest rate = 7.5% /12 = 0.625%
n = no. of payments = 58

Present value of annuity due = P + P * [ (1 - (1+r)^-(n-1)) / r ]
$20,887.80 = P + P * [ (1 - (1+0.00625)^-(58-1)) / 0.00625 ]
$20,887.80 = P + P * [ (1 - (1.00625)^-57) / 0.00625 ]
$20,887.80 = P + P * 47.8281
$20,887.80 = P * 48.8281
P = $427.78

Hence the monthly withdrawl will be $427.78