A student has a savings account earning 8% simple interest. She must pay $1,400 for first-semester tuition by September 1 and $1,400 for second-semester tuition by January 1. How much must she earn in the summer (by September 1) in order to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1,400 between September 1 and January 1? Round your answer to two decimal places.
A) $2,781.58
B) $2,772.55
C) $2,763.64
D) $2,746.15
E) $2,784.18

Question

A student has a savings account earning 8% simple interest. She must pay $1,400 for first-semester tuition by September 1 and $1,400 for second-semester tuition by January 1. How much must she earn in the summer (by September 1) in order to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1,400 between September 1 and January 1? Round your answer to two decimal places. ​
A) $2,781.58
B) $2,772.55
C) $2,763.64
D) $2,746.15
E) $2,784.18

Quizplus · Accepted Answer

To have $1,400 by January 1 with 8% simple interest over 4 months (1/3 of a year), she needs to invest $1,400 / (1 + 0.08 * 1/3) = $1,363.64. Adding the $1,400 needed by September 1, she must earn $1,400 + $1,363.64 = $2,763.64.

A Student Has a Savings Account Earning 8% Simple Interest