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.
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.
