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.

Answer 1

$1,721.31 is the answer to this question  

Answer 2

Carlos pay in service charges is $1721.3

Explanation:

Given : 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.

To find : How much did Carlos pay in service charges?

Solution : First we find the monthly payment of the loan

Formula of monthly payment

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

Discount factor
`D=(1-(1+i)^(-n))/(i)`

Where, Amount = $22,375

Rate r= 5.49%=0.0549 compounded quarterly

`i=(0.0549)/(4)=0.013725`

Time = 7 years

`n=7*4=28`

Now, put all the values we get,

`D=(1-(1+i)^(-n))/(i)`

`D=(1-(1+0.013725)^(-28))/(0.013725)`

`D=(1-(1.013725)^(-28))/(0.013725)`

`D=(1-0.68270)/(0.013725)`

`D=(0.3172)/(0.013725)`

`D=23.1177`

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

`M=(22375)/(23.1177)`

`M=967.871`

Now payment he has for for 7 years compounded quarterly i.e, for 28

Payment = 967.871 × 28 = $27100.39

Service charges = Total payment - payment

= $28,821.67 - $27100.39

= $1721.27

Therefore, Carlos pay in service charges is $1721.3