A new luxury car costs $80,000. You pay 10% down and amortize the rest with equal monthly payments over a 7-year period. If you pay 9.25% compounded monthly, what is your monthly payment? How much interest will you pay?
To find the monthly payment and the amount of interest you'll pay, we need to use the formula for amortized loans. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (remaining balance)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments
Let's calculate it step by step.
Step 1: Calculate the principal amount
You pay 10% down, so the principal amount (P) is 90% of the car's price:
P = 0.9 * $80,000
P = $72,000
Step 2: Calculate the monthly interest rate
The annual interest rate is 9.25%, so the monthly interest rate (r) is:
r = 9.25% / 12
r = 0.0925 / 12
Step 3: Calculate the total number of monthly payments
Since you're making payments over a 7-year period, the total number of monthly payments (n) is:
n = 7 years * 12 months/year
n = 84
Step 4: Calculate the monthly payment
Using the formula above, plug in the values:
M = $72,000 * (0.0925/12 * (1 + 0.0925/12)^84) / ((1 + 0.0925/12)^84 - 1)
Calculating this value gives us: M ≈ $1,107.34 (rounded to the nearest cent)
So, your monthly payment will be approximately $1,107.34.
Step 5: Calculate the total interest paid
To calculate the total interest paid over the loan term, we can multiply the monthly payment by the total number of payments and subtract the principal amount:
Total interest = (M * n) - P
Total interest = ($1,107.34 * 84) - $72,000
Calculating this value gives us: Total interest ≈ $19,769.56 (rounded to the nearest cent)
Therefore, you will pay approximately $19,769.56 in interest over the 7-year period.