Final answer:
Mr. Simons can calculate the annual savings required to meet his retirement goal by using the future value of an annuity formula, adjusted to incorporate his current savings and the compound interest rate of 8%.
Step-by-step explanation:
Mr. Simons needs to determine how much he must save each year to reach his retirement goal of $80,000, starting with his current savings of $25,000 and an interest rate of 8% over the next ten years. To calculate this, we would typically use the future value of an annuity formula, which is FV = Pmt * ((1 + r)^n - 1) / r, where Pmt is the payment (annual savings), r is the rate of interest per period, and n is the number of periods. However, because we need to find the annual savings amount, we must rearrange the formula to solve for Pmt. The equation should incorporate the present value of current savings, which also grows at the rate of 8% per annum. The final calculation would look like this: Pmt = (FV - PV * (1 + r)^n) / ((1 + r)^n - 1) / r), where PV is the present value of the current savings.
By inputting Mr. Simons's numbers into the formula, we determine the annual amount that he needs to save. In this formula, FV ($80,000) is the future value desired, PV ($25,000) is the current savings, r (0.08) is the annual interest rate, and n (10) is the number of years until retirement.