Find the monthly payment, needed to have a sinking fund accumulate the future value, $16,000. The yearly interest rate is 6.7% and the number of payments is 20. Interest is compounded monthly.
I do not remember how to solve for this equation. Please help me.
Would the answer be 223.98?
To find the monthly payment needed to accumulate a future value in a sinking fund, you can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r,
Where:
FV is the future value,
P is the monthly payment,
r is the monthly interest rate, and
n is the number of payments.
In your case, the future value (FV) is $16,000, the monthly interest rate (r) is 6.7% divided by 12 (0.067/12 = 0.00558), and the number of payments (n) is 20.
Now we can rearrange the formula to solve for the monthly payment (P):
P = FV * r / ((1 + r)^n - 1).
Plugging in the values, we get:
P = $16,000 * 0.00558 / ((1 + 0.00558)^20 - 1).
Calculating this expression will give you the monthly payment needed to accumulate the future value of $16,000 in 20 payments with a 6.7% annual interest rate compounded monthly.