You have just finished paying off your $35,125 loan, a feat which took ten years of quarterly payments. The loan had an interest rate of 7.44%, compounded quarterly. If you also paid $5,180.70 in service charges, what percentage of the total cost was made up by your finance charges? Round all dollar values to the nearest cent.

1 answer

First, let's calculate the total amount paid for the loan amount:

Amount paid for loan = $35,125 + $5,180.70 = $40,305.70

Next, let's calculate the total finance charges paid over the course of ten years:

PV = $35,125
r = 7.44% / 4 = 1.86% = 0.0186 quarterly
n = 4 quarters per year * 10 years = 40 quarters

FV = PV * (1 + r)^n
FV = $35,125 * (1 + 0.0186)^40
FV = $35,125 * (1.0186)^40
FV = $35,125 * 1.877
FV = $65,985.64

Total finance charges = $65,985.64 - $35,125 = $30,860.64

Now, let's calculate the percentage of the total cost made up by finance charges:

Total cost = Total amount paid for loan + Total finance charges
Total cost = $40,305.70 + $30,860.64 = $71,166.34

Percentage of total cost made up by finance charges = (Total finance charges / Total cost) * 100
Percentage of total cost made up by finance charges = ($30,860.64 / $71,166.34) * 100
Percentage of total cost made up by finance charges = 43.36%

Therefore, finance charges make up approximately 43.36% of the total cost.