MTH 201 - Quantitative Reasoning 11-2024 Summer

---

Current Objective: Evaluate student loan options

Question:

Jennifer recently finished paying off her [tex]$30,000 fixed-rate student loan. She paid $[/tex]303.73 per month for 10 years to complete the payments. How much interest did she pay over the duration of the loan? Round to the nearest cent.

Provide your answer below:



Answer :

Alright, let's break down the problem step-by-step.

1. Identify the initial loan amount or principal:
- Jennifer's initial loan amount is $30,000.

2. Determine the monthly payment amount:
- Jennifer paid $303.73 each month.

3. Calculate the total number of payments:
- The loan duration is 10 years.
- Since there are 12 months in a year, the total number of monthly payments over 10 years is calculated as follows:
[tex]\[ \text{Total number of payments} = 10 \text{ years} \times 12 \text{ months/year} = 120 \text{ payments} \][/tex]

4. Calculate the total amount paid over the duration of the loan:
- Each of the 120 payments is $303.73.
- Thus, the total amount paid over the duration of the loan is:
[tex]\[ \text{Total amount paid} = 120 \text{ payments} \times \[tex]$303.73 \text{ per payment} = \$[/tex]36,447.60
\][/tex]

5. Determine the total interest paid:
- The total interest paid is the difference between the total amount paid and the initial loan amount (principal).
- So, the total interest paid is:
[tex]\[ \text{Total interest paid} = \text{Total amount paid} - \text{Principal} = \[tex]$36,447.60 - \$[/tex]30,000 = \$6,447.60
\][/tex]

6. Round to the nearest cent:
- The amount is already expressed to the nearest cent.

Therefore, Jennifer paid a total of [tex]$6,447.60 in interest over the duration of her $[/tex]30,000 student loan.