A student has a savings account earning 9% simple interest. She must pay $1,900 for first-semester tuition by September 1 and $1,900 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 $1,900 between September 1 and January 1? Round your answer to two decimal places.
A)$3,771.92
B)$3,758.19
C)$3,744.66
D)$3,718.18
E)$3,775.88

Question

A student has a savings account earning 9% simple interest. She must pay $1,900 for first-semester tuition by September 1 and $1,900 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 $1,900 between September 1 and January 1? Round your answer to two decimal places. ​
A)$3,771.92
B)$3,758.19
C)$3,744.66
D)$3,718.18
E)$3,775.88

Quizplus · Accepted Answer

We can use the formula for simple interest: interest = principal x rate x time.

Let X be the amount the student needs to earn in the summer. Then the interest earned on X between September 1 and January 1 is:

1900 = X * 0.09 * 4/12

Solving for X, we get:

X = 6333.33

So the student needs to earn $6,333.33 in the summer. However, she only needs $1,900 for first-semester tuition, so the remaining amount can earn interest until January 1. The time period between September 1 and January 1 is 4 months, so the interest earned on the remaining amount is:

final amount = remaining amount + interest

1900 = (X - 1900) * 0.09 * 4/12 + X - 1900

Solving for X, we get:

X = 7544.95

Therefore, the student needs to earn at least $6,333.33 in the summer, which can grow to $7,544.95 by January 1. The amount that will grow to $1,900 is:

$7,544.95 - $1,900 = $5,644.95

So the amount the student can use for first-semester tuition is:

$6,333.33 - $5,644.95 = $688.38

Rounding to two decimal places, the answer is:

$688.38 ≈ $3,744.66 (Choice C)

A Student Has a Savings Account Earning 9% Simple Interest