Question

Jessica took out a Stafford loan worth $7,175 at the beginning of her six-year college career. The loan has a duration of ten years and an interest rate of 6. 3%, compounded monthly. How much greater will Jessica’s monthly payment be if the loan is unsubsidized than if the loan is subsidized? Round all dollar values to the nearest cent. A. $36. 98 b. $23. 07 c. $37. 67 d. $166. 37.

Answer 1

The correct statement is that the monthly payment of Jessica will be greater by approximately $10.25 if the loan is unsubsidized than if the loan was subsidized.

The calculation of difference of the monthly payment in each of the cases will be done by comparing the monthly payments in each of the cases of subsidized and unsubsidized loans.

Calculation of Monthly Payments

The formula for calculation of monthly payments of loan ca be ascertained by division of the loan amount with the number of months. The compound interest can be calculated as follows,

$\rm Compounded\ Annuity= P(1+\dfrac{r}{n})^n^t\\\\\rm Compounded\ Annuity= 7175(1+\dfrac{0.063}{12})^1^2^0\\\\\rm Compounded\ Annuity= \ 13449$

Compounded Annuity if the loan was subsidized at 5.28% interest rate.

$\rm Compounded\ Annuity= 7175(1+0.0044)^1^2^0\\\\\rm Compounded\ Annuity= \ 12151$

The monthly payments can be calculated as,

$\rm Unsubsidized\ Monthly\ Payments= \dfrac{13449}{120}\\\\\rm Unsubsidized\ Monthly\ Payments= \ 112$

and

$\rm Subsidized\ Monthly\ Payments= \dfrac{12151}{120}\\\\\rm Subsidized\ Monthly\ Payments=\ 101.75$

So, the difference of the monthly payments is calculated as $10.25 on the subsidization of the Stafford loan.

Hence, the monthly contribution is increased by $10.25 each month if the Stafford Loan taken by Jessica is not subsidized.

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