As you and your spouse are discussing your monthly budget at the dinner table one night, you are both curious as to how much of your $325 car payment is going to principal and how much to interest. Knowing that you are paying an APR of 3.75% to the bank and that you still owe approximately $9,000 on the balance of the loan, calculate both the interest and principal portions of the payment and show your work.
Principal = ______________
Interest = _______________
To calculate the interest and principal portions of your car payment, we need to use the formula for calculating the monthly payment on a loan using the Amortization Formula:
Payment = Principal * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
- Payment is the monthly payment
- Principal is the initial loan amount
- r is the interest rate per period (monthly in this case)
- n is the total number of periods (months in this case)
Let's break down the given information:
Principal: $9,000
APR (Annual Percentage Rate): 3.75%
Monthly interest rate (r): APR / 12
Number of periods (n): Total number of months for the loan term (unknown in this case)
Now, let's calculate the monthly payment first:
r = 3.75% / 12 = 0.003125 (monthly interest rate)
We know the monthly payment is $325. Rearranging the Amortization Formula to solve for Principal gives us:
Principal = Payment / ((r * (1 + r)^n) / ((1 + r)^n - 1))
Substituting the given values:
$325 = Principal / ((0.003125 * (1 + 0.003125)^n) / ((1 + 0.003125)^n - 1))
We can solve this equation to find the value of n (number of months) using trial and error or numerical methods like a spreadsheet or calculator.
After finding the value of n, we substitute it back into the formula to calculate the Principal and Interest portions of the payment.
Let's solve the equation to find the value of n.