QuestionJuly 18, 2025

A student is graduating from college in 12 months but will need a loan in the amount of 7,685 for the last two semesters. The student receives an unsubsidized Stafford Loan with an interest rate of 6.2% compounded monthly, and a payment grace period of six months from the time of graduation. After the grace period the student makes fixed monthly payments of 163.21 for five years. Determine the total amount of interest the student paid. 2,149.29 1,158.81 2,107.60 1,186.17

A student is graduating from college in 12 months but will need a loan in the amount of 7,685 for the last two semesters. The student receives an unsubsidized Stafford Loan with an interest rate of 6.2% compounded monthly, and a payment grace period of six months from the time of graduation. After the grace period the student makes fixed monthly payments of 163.21 for five years. Determine the total amount of interest the student paid. 2,149.29 1,158.81 2,107.60 1,186.17
A student is graduating from college in 12 months but will need a loan in the amount of 7,685 for the last two semesters. The student receives an unsubsidized Stafford Loan with an interest rate of 6.2% compounded monthly, and a payment grace period of six months from the time of graduation. After the grace period the student makes fixed monthly payments of 163.21 for five years. Determine the total amount of interest the student paid. 2,149.29 1,158.81 2,107.60 1,186.17

Solution
4.0(264 votes)

Answer

\2,107.60 Explanation 1. Calculate the loan amount after grace period The loan is compounded monthly for 18 months (12 months until graduation + 6 months grace period). Use **A = P(1 + \frac{r}{n})^{nt}** where P = 7685, r = 0.062, n = 12, t = 1.5. \[ A = 7685 \times \left(1 + \frac{0.062}{12}\right)^{12 \times 1.5} \] 2. Calculate total payment over five years Monthly payments are made for 60 months. Total payment = 163.21 \times 60. 3. Calculate total interest paid Subtract the original loan amount from the total payment to find the total interest. \[ \text{Total Interest} = (\text{Total Payment}) - (\text{Loan Amount after Grace Period}) \]

Explanation

1. Calculate the loan amount after grace period<br /> The loan is compounded monthly for 18 months (12 months until graduation + 6 months grace period). Use **$A = P(1 + \frac{r}{n})^{nt}$** where $P = 7685$, $r = 0.062$, $n = 12$, $t = 1.5$. <br />\[ A = 7685 \times \left(1 + \frac{0.062}{12}\right)^{12 \times 1.5} \]<br /><br />2. Calculate total payment over five years<br /> Monthly payments are made for 60 months. Total payment = $163.21 \times 60$.<br /><br />3. Calculate total interest paid<br /> Subtract the original loan amount from the total payment to find the total interest.<br />\[ \text{Total Interest} = (\text{Total Payment}) - (\text{Loan Amount after Grace Period}) \]
Click to rate:

Similar Questions