We use the future value of an ordinary annuity formula because equal deposits are made every month.
Step 1: Identify the information given.
Future value (FV) = $89,000
Annual interest rate = 4.8% = 0.048
Monthly interest rate = 0.048 / 12 = 0.004
Time = 16 years
Number of monthly deposits = 16 x 12 = 192
Monthly deposit (PMT) = Unknown
Step 2: Write the formula.
FV = PMT x [(1 + r)^n - 1] / r
Rearrange to solve for PMT:
PMT = FV x r / [(1 + r)^n - 1]
Step 3: Substitute the values.
PMT = 89,000 x 0.004 / [(1.004)^192 - 1]
PMT = 356 / [(1.004)^192 - 1]
Step 4: Calculate.
PMT = 308.9871...
Rounded to the nearest cent:
PMT = $308.99
Final Answer: You should deposit $308.99 each month to accumulate $89,000 in 16 years at 4.8% interest compounded monthly.
This assumes deposits are made at the end of each month and the account begins with a zero balance.
