You are considering two savings options. Both options offer a rate of return of 7.6 percent. The first option is to save $2,500, $2,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?

Question

Quizplus · Accepted Answer

To find the equivalent lump sum amount that needs to be saved today to have the same balance at the end of three years as the first option, we calculate the future value of each annual saving and then find the present value of the total future value at the given rate of 7.6%. The future value of the savings at the end of three years can be calculated using the formula FV = P * (1 + r)^n, where P is the principal amount, r is the annual interest rate, and n is the number of years. Then, to find the present value of this total future value, we use the formula PV = FV / (1 + r)^n. Calculating the future values of each saving and discounting them back to the present at 7.6% will give us the lump sum amount needed today, which matches option D, $6,890.89.

You Are Considering Two Savings Options