How can we calculate the size of the quarterly payment, the total amount of the payment, and the total amount of interest paid on a house purchase when given the parameters of the purchase price, down payment, interest rate, and repayment period?

Question

Davin · Answer

The size of the quarterly payment, the total amount of the payment, and the total amount of interest paid on a house purchase can be calculated using the formula for the present value of an annuity. This formula takes into account the debt amount, quarterly payment, annual interest rate, number of compounding periods per year, and total number of years for repayment.  To find the quarterly payment, we use the formula:  PV = P * [1 - (1 + r/n)^(-n*t)] / (r/n)   Where:  PV = present value of the debt  P = quarterly payment  r = annual interest rate  n = number of compounding periods per year  t = total number of years  By substituting the given values ($150,000 debt, 12% annual interest rate, 4 compounding periods per year, 10-year repayment period) into the formula, we can calculate the quarterly payment to be approximately $218,716.83.  To find the total amount of the payment, we multiply the quarterly payment by the total number of payments over the repayment period. In this case, the total amount of the payment is calculated to be $8,748,673.20.  Finally, to determine the total amount of interest paid, we subtract the original debt from the total payments. The total interest paid on this house purchase is calculated to be $8,598,673.20.  In summary, by utilizing the formula for the present value of an annuity, we can determine the size of the quarterly payment, the total amount of the payment, and the total amount of interest paid on a house purchase.

Calculating Quarterly Payment, Total Payment, and Total Interest on a House Purchase

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