Question

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 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, the student must earn at least $38.67 in the summer.

Step-by-step explanation:

To calculate how much the student must earn in the summer 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, we can use the simple interest formula. Here are the steps:

1. Calculate the amount needed by September 1: $1400
2. Calculate the time between September 1 and January 1: 4 months
3. Calculate the interest rate: 9% = 0.09
4. Calculate the amount that will grow to $1400 in 4 months: $1400 / (1 + 0.09/12)^(4)
5. Subtract the amount needed by September 1 from the amount calculated in step 4 to find how much the student must earn in the summer.

Let's calculate:

1. Amount needed by September 1: $1400
2. Time between September 1 and January 1: 4 months
3. Interest rate: 9% = 0.09
4. Amount that will grow to $1400 in 4 months: $1400 / (1 + 0.09/12)^(4) = $1361.33
5. Amount the student must earn in the summer: $1361.33 - $1400 = -$38.67

Therefore, the student must earn at least $38.67 in the summer 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.

Answer 2

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.