Explanation:
To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:
PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)
where:
- PV is the present value of the annuity due ($32,000)
- PMT is the monthly payment we want to find
- r is the annual interest rate (7.9%)
- n is the number of times interest is compounded per year (12 for monthly compounding)
- t is the number of years (10)
PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**
Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.