Hong le buys a car costing $14,000. he agrees to make payments at the end of each monthly period for 4 years. he pays 7% interest, compounded monthly.
a. what is the amount of each payment?
b. find the total amount of interest le will pay

Answers

Answer 1
Use the formula of the present value of an annuity ordinary to find the monthly payment
The formula is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 14000
PMT monthly payment?
R interest rate 0.07
K compounded monthly 12
N time 4years
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=14,000÷((1−(1+0.07÷12)^(
−12×4))÷(0.07÷12))
=335.25

Total payments
335.25×12 months×4years
=16,092

Total amountof interest
16,092−14,000
=2,092

Hope it helps!
Answer 2
Final answer:

The monthly payment is approximately $334.7 and the total interest paid over the loan term is approximately $2,065.6. This was calculated using the formula for an annuity loan and using details provided in the question.

Explanation:

This is a question about loan repayment and involves calculating both the monthly payment and the total amount of interest paid over the loan term. To calculate the monthly payments, we can use the formula for an annuity loan: P = [r*PV] / [1 - (1 + r)^-n], where P stands for payment, r is the monthly interest rate, PV is the present value, and n is the number of payments.

First, convert the annual 7% interest rate into a monthly rate by dividing by 12, giving an r value of 0.007. The present value (PV) is the loan amount of $14,000 and the number of payments (n) is the total number of months in 4 years, which is 48. Substituting these values, we get P = [0.007 * 14000] / [1 - (1 + 0.007)^-48] = around $334.7.

For the total interest paid, multiply the monthly payment by the total number of payments and subtract the original loan amount. So, total interest = $334.7 * 48 - $14,000 = around $2,065.6.

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