Question

Paul has an eight-year loan with a principal of $26,900. The loan has an interest rate of 8. 18%, compounded quarterly. If Paul pays $1,527 in service charges and makes quarterly payments on his loan, what will his total finance charge be when the loan is repaid? Round all dollar values to the nearest cent. A. $10,588. 28 b. $11,546. 36 c. $11,370. 04 d. $1,527. 0.

Answer 1

The total finance charge would be $11,546. 36 when the loan is repaid.

The rate of interest is 8.18% or 0.0818 compounded quarterly (4) that would determine the value if i that is interest by:

$\frac{0.0818 }{4} \\=0.02045$

Now, the number of years or n is computed as:

$8*4\\=32$

Here, 8 is time/year and 4 is quarterly interest payment.

The discounting factor is calculated below:

$D=\frac{1-(1+i)^{-n} }{i} \\=\frac{1-(1+0.02045)^{-32} }{0.02045} \\=23.31$

Now, we will calculate the quarterly payment by:

$\frac{26900}{23.31} \\=1153.76$

The payment made in 8 years quarterly would be:

$1153.76*32\\= 36920.32$

It would lead us to compute interest amount in total paid as:

$36921.32 - 26900\\= 10021.32$

Hence, financial charge is derived by adding the total interest and service charge, that is,

$10021.32 + 1527 = 11548.32$

Here, to convert the financial charge amount in cents by calculating the charge amount with 100, which would give 1154832 cents loan amount payment.

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