Question

A student has a savings account earning 3% simple interest. She must pay $1200 for first-semester tuition by September 1 and $1200 for second-semester tuition by January 1. How
much must she earn in the summer (by September 1) to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1200 between September 1
and January 1? (Round your answer to the nearest cent.)

Answer 1

Using simple interest, it is found that she needs to earn $2,391.07 during the summer.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

• A(0) is the initial amount.

• r is the interest rate, as a decimal.

For this problem, the objective is to have $1200 in 3 months = 0.25 years, hence the parameters are given as follows:

A(0.25) = 1200, t = 0.25, r = 0.03.

Hence we have to solve for A(0):

A(0)(1 + 0.03 x 0.25) = 1200

A(0) = 1200/(1 + 0.03 x 0.25)

A(0) = $1,191.07.

She also needs to earn $1,200 to pay the first-semester bill on time, hence:

1200 + 1191.07 = $2,391.07.

She needs to earn $2,391.07 during the summer.

More can be learned about simple interest at brainly.com/question/16646150

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