Question

Carlos took seven years to pay off his loan by making identical quarterly payments. The loan had a principal of $22,375 and 5. 49% interest, compounded quarterly. Carlos paid a total of $28,821. 67. How much did Carlos pay in service charges? Round all dollar values to the nearest cent. A. $1,721. 31 b. $4,725. 36 c. $1,670. 98 d. $6,446. 67.

Answer 1

Carlos pays service charges of $1,721. 31 while paying off the loan amount.

The principle amount is given as $22,375 at 5.49% interest or 0.0549. It needs to be compounded quarterly, which is in 4 months for 7 years.

The interest amount would be:

$\frac{ 0.0549}{4} \\=0.013725$

The value of n is computed as:

$n=T*4\\=7*4\\=28$

Therefore, the discount factor is derived as follows:

$D=\frac{1-(1+i)^{n} }{i} \\=\frac{1-(1+0.013725)^{28} )}{0.013725} \\=23.1177$

Here, the monthly payment is calculated by:

$M=\frac{Amount}{D}\\=\frac{22375}{23.1177} \\=967.87$

Thus, the final payment for 7 years that is compounded quarterly would be:

$967.871*28\\=27100.39$

The service charge here would be:

$28,821.67-27100.39\\=1721.27$

Hence, the service charge is 1721.27 by deducting the final payment from the total payment.

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