We can use the formula for the future value of an annuity again, but this time we need to solve for the payment amount, given the future value we want to accumulate. The formula is:
Pmt = FV x (r / ((1 + r)^n - 1))
where:
Pmt is the monthly payment we need to make
FV is the future value we want to accumulate (which is $15,000 in this case)
r is the monthly interest rate, which we can calculate as APR / 12 (since APR is the annual interest rate)
n is the total number of payments we will make, which is the number of years times 12 (since there are 12 months in a year)
Substituting the given values, we get:
Pmt = $15,000 x (0.065/12) / ((1 + 0.065/12)^(9*12) - 1)
Pmt = $15,000 x 0.00541667 / (1.92449 - 1)
Pmt = $15,000 x 0.00541667 / 0.92449
Pmt = $87.63 (rounded to the nearest cent)
Therefore, you need to deposit $87.63 per month to accumulate $15,000 in 9 years at an APR of 6.5%.