A student takes out a loan of $12,360 at a fixed APR of 5.5% for 5 years.
a) What is the monthly payment? (Round to the nearest cent as needed)
b) What is the total amount paid over the term of the loan? (Round to the nearest cent as needed)
c) Of the total amount paid, what percentage is paid toward the principal? (Round to the nearest tenth of a percent)
d) Of the total amount paid, what percentage is paid toward interest? (Round to the nearest tenth of a percent)
To calculate the monthly payment, total amount paid, and the percentages paid toward the principal and interest, we will use the formula for calculating a fixed monthly payment on a loan:
Monthly Payment = [P x (r(1+r)^n)] / [(1+r)^n-1]
Where:
P = Principal loan amount
r = Monthly interest rate (Annual interest rate divided by 12)
n = Total number of monthly payments (terms)
a) Calculating the monthly payment:
Principal amount (P) = $12,360
Annual Percentage Rate (APR) = 5.5%
Monthly interest rate (r) = APR / 12
Number of years (n) = 5
Number of monthly payments (n) = n x 12
Using these values in the formula:
r = 5.5% / 12 = 0.004583 (monthly interest rate)
n = 5 x 12 = 60 (number of monthly payments)
Monthly Payment = [12,360 x (0.004583 (1+0.004583)^60)] / [(1+0.004583)^60-1]
= 243.10
Therefore, the monthly payment is $243.10 (rounded to the nearest cent).
b) Calculating the total amount paid over the term of the loan:
Total Amount Paid = Monthly Payment x Number of Monthly Payments
Total Amount Paid = $243.10 x 60
= $14,586
Therefore, the total amount paid over the term of the loan is $14,586 (rounded to the nearest cent).
c) Calculating the percentage paid toward the principal:
Principal Portion = Monthly Payment x Number of Monthly Payments - Principal Amount
Principal Portion = $243.10 x 60 - $12,360
= $14,586 - $12,360
= $2,226
Percentage Paid toward Principal = (Principal Portion / Total Amount Paid) x 100
Percentage Paid toward Principal = ($2,226 / $14,586) x 100
= 15.24%
Therefore, approximately 15.2% (rounded to the nearest tenth of a percent) of the total amount paid goes toward the principal.
d) Calculating the percentage paid toward interest:
Interest Portion = Total Amount Paid - Principal Portion
Interest Portion = $14,586 - $2,226
= $12,360
Percentage Paid toward Interest = (Interest Portion / Total Amount Paid) x 100
Percentage Paid toward Interest = ($12,360 / $14,586) x 100
= 84.76%
Therefore, approximately 84.8% (rounded to the nearest tenth of a percent) of the total amount paid goes toward interest.