Final answer:
The future value of $53,100 receivable at the end of each period for 8 periods compounded at 12% is calculated by applying the compound interest formula for each payment across the remaining periods and summing the results.
Step-by-step explanation:
To calculate the future value of $53,100 receivable at the end of each period for 8 periods compounded at 12%, one would typically use the formula for the future value of an annuity. However, since the question is structured to calculate each payment separately rather than as a stream of payments, the specific formula used considers each $53,100 payment growing at the compound interest rate of 12% for the remaining periods until the end.
For each $53,100 payment, the future value (FV) can be found using the formula:
FV = Principal × (1 + interest rate)time
However, it's important to note that this formula applies to each individual $53,100 payment made at the end of each period. If we were to consider all eight $53,100 payments made at the end of each period, we would need to use the future value of an annuity formula, which is different and incorporates all payments over time.
To illustrate with a simple example, if we had a single payment of $53,100 compounded at 12% for 1 year, the future value would be:
FV = $53,100 × (1 + 0.12)1 = $53,100 × 1.12
In practice, you would calculate the future value of each $53,100 payment at the end of each period considering how many periods remain for each and then sum them up to get the total future value.