Question

Suppose you borrow $40,000 at 13% (.13) APR for a 12-year term to be paid monthly.

Your monthly payment is $450.00. How much of your first payment goes toward
interest?
Interest allocation formula if needed:

pays in a year
x principal = interest

Answer 1

The interest portion of the first payment is $433.20.

Explanation:

To find out how much of your first payment will go to interest, we need to calculate the monthly interest rate and then use it to calculate the interest portion of the monthly payment.

First, we need to calculate the monthly interest rate by dividing the annual interest rate by 12.

Annual interest rate = 13%

Monthly interest rate = 13%/12 = 0.01083

Next, we can use the monthly payment amount and the monthly interest rate to calculate the interest portion of the payment:

Interest portion of payment = Monthly interest rate x Remaining loan balance

To calculate the remaining loan balance after the first payment, we can use the formula for the present value of an ordinary annuity:

Remaining loan balance = Present value of remaining payments

Present value of remaining payments = Monthly payment x (1 - (1 + monthly interest rate)^-n) / monthly interest rate

where n is the total number of payments over the term of the loan.

n = 12 years x 12 months/year = 144 payments

Present value of remaining payments = $450 x (1 - (1 + 0.01083)^-144) / 0.01083 = $44,373.68

Remaining loan balance after first payment = $44,373.68 - $40,000 = $4,373.68

Finally, we can calculate the interest portion of the first payment:

Interest portion of payment = 0.01083 x $40,000 = $433.20

Therefore, the interest portion of the first payment is $433.20.