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.
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.