Question

Gertrude takes out a $5,500 subsidized Stafford loan, which must be paid back in ten years. Gertrude will graduate four years after taking out the loan. If the loan has an interest rate of 6. 8%, compounded monthly, and Gertrude makes monthly payments, how much interest will she pay by the time the loan is repaid? Round all dollar values to the nearest cent. A. $4,462. 40 b. $1,213. 28 c. $1,713. 69 d. $2,094. 80.

Answer 1

The interest is the amount of payment that is given by the borrower to the lender of money, it is the excess amount that is paid for the use of money.

The amount of interest that Gertrude would pay is $2,908 to repay the total amount of the loan.

What is interest?

Interest is the monetary charge for acquiring money, and it is mostly shown as a percentage, such as an annual percentage rate (APR).

Interest is the excess amount that is paid by the lender to use his money on a certain percentage, and it is repaid with the amount of principal.

Computation of Interest:

Given that,

Principal(P) = $5,550,

Interest Rate(i) = 6.8%,

$\text{i} = \dfrac{6.8}{12\times100}\\\\\text{i} =0.005667$

Number of monthly Installments(n)= 10×12 = 120.

Here, we apply the formula of E.M.I (Equated Monthly Installment):

$\text{E.M.I.}= \dfrac{P\times i\times (1+i)^n}{(1+i)^n-1}\\\\\\\text{E.M.I.}=\dfrac{\ 5,500\times 0.005667\times (1+0.005667)^1^2^0}{(1+0.005667)^1^2^0-1}\\\\\\\text{E.M.I.}=\ 63.29$

Here, the total installments of the loan are 120,

then the amount of total payment would be:

$120\times\ 63.29= \ 7,594$

Then, the amount of interest that is paid on the loan would be:

$\text{Amount -Principal}= \text{Interest}\\\\\ 7,594.28-\ 5,500= \ 2,094.28\\\\\\\text{Interest}= \ 2,094.28$

Therefore, the total amount of interest that Gertrude has to pay is $2,097.28.

Learn more about interest, refer to:

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