A student has a savings account earning 9% simple interest. She must pay $1400 for first-semester tuition by September 1 and $1400 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 $1400 between September 1 and January 1? (Round your answer to the nearest cent.)

Answer: The answer is $2,759.22

Explanation: From the question above, we have:

September 1st to January 1st is 4 months, this is 1/3 of a year which means that the student will earn:

=> 9/3 = 3%

3% interest for the money that is saved is the savings account. So the student must put in at least:

x + 3%x = 1400

x + 0.03x = 1400

1.03x = 1400

x = 1400 / 1.03

x = 1,359.22

Therefore, if the student saves $1,359.22 in the savings account By September 1st, she will have $1400 by January 1st.

Also, the student needs to make $1400 for the first semester. So overall she will need to make:

1,400 + 1,359.22 = $2,759.22 during the summer in order to ensure that she will have enough money to pay for both semesters.