Bobby's parents loaned him $80,000 to fund his college education.His parents are not charging interest.They desire to be paid one lump sum of $80,000 when Bobby can accumulate that amount.Bobby established a savings plan that earns 8% compounded annually.His new job promises to pay an annual holiday bonus that will enable him to make equal annual,year-end deposits of $6,400 starting next year.Approximately how many years will it take Bobby to accumulate the $80,000?

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity to solve this problem:
FV = Pmt x (((1 + r)^n - 1) / r)
Where FV is the future value we want to achieve ($80,000), Pmt is the annual deposit ($6,400), r is the annual interest rate (8%), and n is the number of years.
Plugging in the numbers, we get:
$80,000 = $6,400 x (((1 + 0.08)^n - 1) / 0.08)
Simplifying and solving for n, we get:
n ≈ 8.96
Therefore, it will take Bobby approximately 9 years to accumulate $80,000.

Bobby's Parents Loaned Him $80,000 to Fund His College Education