You would like to buy a Mazda Miata Convertible for a purchase price of $27,500. You will take out a loan for the entire amount. a. You have excellent credit so you can secure a loan at 5% APR for 3 years. What is your monthly payment? How much will you pay in interest if you pay off the loan as scheduled? b. Now suppose instead you want to consider a 5 year loan at 6.5% APR. What is your monthly payment? How much will you pay in interest if you pay off the loan as scheduled? c. Compare the cost of the two loans.
Use same Eq I used in your 12:38 AM post.
a. To calculate the monthly payment for the loan, we can use the formula for the fixed monthly payment of a loan:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal amount (the purchase price of $27,500)
r = Monthly interest rate (APR divided by 12 and then divided by 100)
n = Total number of monthly payments (3 years = 36 months)
First, let's calculate the monthly interest rate:
APR = 5%
Monthly interest rate = 5% / 12 / 100 = 0.0042
Now, we can plug in the values to calculate the monthly payment:
Monthly Payment = $27,500 * 0.0042 * (1 + 0.0042)^36 / ((1 + 0.0042)^36 - 1)
Using a calculator, the monthly payment for the 3-year loan is approximately $826.02.
To find out how much interest you will pay if you pay off the loan as scheduled, we can subtract the principal amount from the total amount paid over the loan term:
Total Interest = (Monthly Payment * n) - P
Total Interest = ($826.02 * 36) - $27,500
Using a calculator, the total interest paid for the 3-year loan is approximately $3,036.72.
b. Following the same steps, but using the updated loan terms:
APR = 6.5%
Monthly interest rate = 6.5% / 12 / 100 = 0.00542
n = 5 years = 60 months
Monthly Payment = $27,500 * 0.00542 * (1 + 0.00542)^60 / ((1 + 0.00542)^60 - 1)
Using a calculator, the monthly payment for the 5-year loan is approximately $540.16.
Total Interest = (Monthly Payment * n) - P
Total Interest = ($540.16 * 60) - $27,500
Using a calculator, the total interest paid for the 5-year loan is approximately $6,409.60.
c. To compare the cost of the two loans, we can simply compare the total interest paid for each loan.
For the 3-year loan, the total interest is approximately $3,036.72.
For the 5-year loan, the total interest is approximately $6,409.60.
Comparing the two, it is clear that the 3-year loan is more cost-effective in terms of interest paid.