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

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value of the annuity, $P$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of periods. We rearrange the formula to solve for $n$, the number of years it will take Jackie to accumulate $80,000. Given $P = $6,400$, $r = 0.08$ (8%), and $FV = $80,000$, we can solve for $n$. Plugging the values into the formula and solving for $n$ gives us approximately 9 years.

Jackie's Parents Loaned Her $80,000 to Fund Her College Education