You plan to purchase an $100,000 house using a 15-year mortgage obtained from yo

Question

You plan to purchase an $100,000 house using a 15-year mortgage obtained from your local bank. The mortgage rate offered to you is 4.5 percent. You will make a down payment of 10 percent of the purchase price.
Calculate the amount of interest and, separately, principal paid in the 80th payment

Calculate the amount of interest and, separately, principal paid in the 110th payment.

Please show work

Calculate the amount of interest and, separately, principal paid in the 110th payment.

Please show work

Explanation / Answer

Monthly Payment on the Mortgage :
P = L[c(1 + c)n]/[(1 + c)n - 1]

Where, P = Monthly Payment,
L = Loan Amount => $90,000
C = Monthly Interest Rate => 4.5%/12 = 0.375%
n = Number of months. => 15 x 12 = 180 Months

Remaining Loan balance after P months:
B = L[(1 + c)n - (1 + c)p]/[(1 + c)n - 1]

After 80 Months:
=> $90,000[(1+0.375%)180-(1+0.375%)80]/[(1+0.375%)180-1] = $57,324.65

After 110 Months:
=> $90,000[(1+0.375%)180-(1+0.375%)110]/[(1+0.375%)180-1] = $42,318.68

Now, total payment made in the 80th month = $688.49 x 80 = $55,079.2
Total Payment made in the principal = $90,000 - $57,324.65 = $32,675
Total Interest Paid = $55,079.2 - $32,675 = $22,403.85

Total payment made in the 110th month = $688.49 x 110 = $75,733.90
Total Payment made in the principal = $90,000 - $42,318.68 = $47,681.32
Total Interest Paid = $75,733.90 - $47,681.32 = $28,052.58

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