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.

Given : 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

To find : What will his total finance charge be when the loan is repaid? Round all dollar values to the nearest cent.

Solution :

Quarterly payment, $Q=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $26,900

Rate r= 8.18%=0.0818 compounded quarterly

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

Time = 8 years

$n=8\times4=32$

Now, put all the values we get,

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

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

$D=\frac{1-(1.02045)^{-32}}{0.02045}$

$D=\frac{1-0.5231}{0.02045}$

$D=\frac{0.47680}{0.02045}$

$D=23.315$

Quarterly payment, $Q=\frac{\text{Amount}}{\text{Discount factor}}$

$Q=\frac{26900}{23.315}$

$Q=1153.76$

Now payment he has for for 8 years compounded quarterly i.e, for 32 months

Payment = 1153.76 × 32 = $36920.32

Total interest = Payment - amount

= 36921.32 - 26900

= $10021.32

Finance charge = Total interest + service charge

= 10021.32 + 1527

= $11548.32

1 dollar = 100 cents

$11548.32 = 11548.32 × 100 = 1154832 cents

Total finance charge be when the loan is repaid is 1154832 cents.