Marie can afford a $250 per month car payment. She’s found a 5 year loan at 7%
interest.
a. How expensive of a car can she afford?
b. How much total money will she pay the loan company?
c. How much of that money is interest?
20. Marie can afford a $250 per month car payment. She’s found a 5 year loan at 7% interest.
a. How expensive of a car can she afford?
b. How much total money will she pay the loan company?
c. How much of that money is interest?
To answer these questions, we need to calculate the monthly car payment, the total amount paid over the loan term, and the interest paid.
a. To determine how expensive of a car Marie can afford, we need to calculate the maximum monthly car payment based on her budget of $250 per month.
b. To find the total amount of money Marie will pay to the loan company, we need to calculate the monthly payment over the 5-year loan term and multiply it by the total number of months in 5 years (60 months).
c. To calculate the amount of interest paid, we subtract the original loan amount from the total amount paid to the loan company.
Let's break down each step of the calculation:
Step 1: Calculate the monthly car payment
To calculate the monthly car payment, we can use the loan formula where M is the monthly payment, P is the principal loan amount, r is the monthly interest rate, and n is the total number of payments (in months).
M = P * (r(1+r)^n) / ((1+r)^n - 1)
P = Principal loan amount (unknown)
r = Monthly interest rate (7% divided by 12 months)
n = Total number of payments (5 years = 60 months)
M = Monthly payment ($250)
We can rearrange the formula to solve for P:
P = M * ((1+r)^n - 1) / (r(1+r)^n)
By substituting the given values into the formula, we can solve for P:
P = 250 * ((1 + 0.07/12)^60 - 1) / ((0.07/12)(1 + 0.07/12)^60)
Step 2: Calculate the total amount paid to the loan company
The total amount paid to the loan company can be found by multiplying the monthly payment (M) by the total number of payments (n).
Total amount paid = M * n
Step 3: Calculate the amount of interest paid
To find the interest paid, we subtract the original loan amount (P) from the total amount paid to the loan company.
Interest paid = Total amount paid - P
Now, let's calculate each part:
a. How expensive of a car can she afford?
To calculate the principal loan amount, we substitute the given values into the formula:
P = 250 * ((1 + 0.07/12)^60 - 1) / ((0.07/12)(1 + 0.07/12)^60)
b. How much total money will she pay the loan company?
To find the total amount paid, we multiply the monthly payment (M) by the total number of payments (n):
Total amount paid = 250 * 60
c. How much of that money is interest?
To calculate the amount of interest paid, we subtract the principal loan amount (P) from the total amount paid:
Interest paid = Total amount paid - P
By performing these calculations, we can determine the answers to all three questions.
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a. To determine how expensive of a car Marie can afford, we need to calculate the loan amount using the formula for a fixed monthly payment:
Loan Amount = Monthly Payment / Monthly Interest Rate
The monthly interest rate can be calculated by dividing the annual interest rate by 12 (number of months in a year), and expressing it as a decimal:
Monthly Interest Rate = Annual Interest Rate / 12
Plugging in the given values:
Monthly Interest Rate = 7% / 12 = 0.07 / 12 = 0.00583
Then, we can calculate the loan amount:
Loan Amount = $250 / 0.00583 ≈ $42,901.98
Marie can afford a car with a maximum price of approximately $42,901.98.
b. To find the total money Marie will pay the loan company, we need to calculate the total number of payments over the 5-year loan term:
Total number of payments = Number of years × 12
Total number of payments = 5 × 12 = 60 payments
The total money paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:
Total money paid = Monthly Payment × Total number of payments
Total money paid = $250 × 60 = $15,000
Marie will pay a total of $15,000 to the loan company.
c. To find out how much of that money is interest, we can subtract the loan amount from the total money paid:
Interest paid = Total money paid - Loan amount
Interest paid = $15,000 - $42,901.98 ≈ -$27,901.98
Therefore, Marie will pay approximately -$27,901.98 in interest.