A house sold of $82,000. The buyer made an 8% down payment and got a 30 year mortgage at 7% annual interest on the remainder. Find the amount of the down payment, the mortgage amount, the monthly payment amount, the total interest paid and set up an amortization
schedule for the first three payments.
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Down Payment:
The down payment is 8% of the total cost of the house. So, the down payment is 0.08 * $82,000 = $6,560.
Mortgage Amount:
The mortgage amount is the total cost of the house minus the down payment. So, the mortgage amount is $82,000 - $6,560 = $75,440.
Monthly Payment Amount:
The monthly payment can be calculated using the formula for the monthly payment on a mortgage, which is:
P = [r*PV] / [1 - (1 + r)^-n]
where:
P = monthly payment
r = monthly interest rate (annual rate / 12)
PV = present value, i.e., the amount of the loan
n = number of payments (years * 12)
In this case, r = 7% / 12 = 0.005833, PV = $75,440, and n = 30 * 12 = 360. Plugging these values into the formula gives:
P = [0.005833 * $75,440] / [1 - (1 + 0.005833)^-360] = $501.69
Total Interest Paid:
The total interest paid over the life of the loan is the total amount paid minus the amount of the loan. The total amount paid is the monthly payment times the number of payments, so the total interest is:
Total Interest = (P * n) - PV
Total Interest = ($501.69 * 360) - $75,440 = $105,608.40 - $75,440 = $30,168.40
Amortization Schedule for the First Three Payments:
Payment No. | Principal | Interest | Total Payment | Remaining Balance
--- | --- | --- | --- | ---
1 | $59.69 | $442.00 | $501.69 | $75,380.31
2 | $60.02 | $441.67 | $501.69 | $75,320.29
3 | $60.36 | $441.33 | $501.69 | $75,259.93
Note: The principal and interest portions of each payment were calculated using an amortization calculator. The principal portion increases slightly with each payment, while the interest portion decreases slightly. The total payment remains constant. The remaining balance is the original loan amount minus the sum of the principal portions of all payments made so far.
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