MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

The Carlos pay in service charges is $1721.3 We have given that the 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.P=22375 and interest rate =5.49%Carlos paid a total of $28,821.67. We have to find how much did Carlos pay in service charges First we find the monthly payment of the loanWhat is the formula of monthly payment?The formula for monthly payment is,[tex]M=\frac{amount}{discount}[/tex]Discount factor [tex]P=\frac{1-(1+i)^{-n}}{i} \\[/tex]Where, Amount = $22,375 and r=0.0549 and compounded quarterly therefore n=4[tex]i=r/n=0.0599/4[/tex]i=0.0137Time =7 years[tex]n=4\times 7=28[/tex]Now put all the values in above formula we get[tex]P=\frac{1-(1+0.01372)^{-28}}{0.01372}\\\\P=\frac{1-(1+0.1372)^{-28}}{0.01372}\\\\P=\frac{1-0.6827}{0.01372}\\\\P=\frac{0.3172}{0.01372}\\\\P=23.11[/tex]Monthly payment, Use the value in the formula of monthly payment[tex]M=\frac{22375}{23.1177}[/tex][tex]M=967.871[/tex]The payment he has for for 7 years compounded quarterly that is for 28Therefore the payment, [tex]Payment= 967.871 \times 28 = $27100.39[/tex][tex]Service charges = Total payment - payment[/tex] [tex]= $28,821.67 - $27100.39[/tex] [tex]= $1721.27[/tex]Therefore, Carlos pay in service charges is $1721.3To learn more about the monthly payment visit: