Final answer:
The question addresses calculating the future value of an annuity with monthly payments under a compound interest rate compounded semiannually. However, because the compounding and payment periods don't align, a standard formula can't be easily applied and a financial calculator or specific software would typically be needed.
Step-by-step explanation:
The question asks for the future value of a series of monthly payments that are being invested in a fund earning compound interest. To find the future value (FV) of an annuity investment where payments (PMT) are made each period, we use the formula: FV = PMT × ((1 + r/n)^(nt) - 1) / (r/n), where PMT is the recurring payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
- In this scenario, the monthly payment (PMT) is $5,300.
- The annual interest rate (r) is 7.00% or 0.07 when expressed as a decimal.
- The interest is compounded semiannually, so n is 2.
- The time period (t) is 4 years.
Before we apply the formula, we need to adjust the interest rate and the number of compounding periods to reflect the monthly payments. The monthly interest rate is not directly given because the compounding is semiannual, and this complicates the calculation because the interest periods don't align with the payment periods.