Question

Some friends tell you that they paid $36,655 down on a new house and are to pay $764 per month for 30 years. If interest is 6.6% compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?

Selling price of the house: $______ (Round to two decimal places as needed.)
Total interest paid: $______ (Round to two decimal places as needed.)
a) $53,217.85; $16,562.85
b) $53,217.85; $36,655.00
c) $70,319.24; $16,562.85
d) $70,319.24; $36,655.00

Answer 1

The selling price of the house, determined by the future value of monthly payments and the down payment, is $172,815.15. The total interest paid is $136,160.15, calculated by subtracting the down payment from the future value.

Step-by-step explanation:

To find the selling price of the house, we need to calculate the future value of the monthly payments plus the initial down payment. We can use the formula for the future value of an ordinary annuity: Future Value = Monthly Payment * (1 + Interest Rate/12)^Total Number of Payments. Plugging in the values, we get Future Value = $764 * (1 + 0.066/12)^(30*12) = $172,815.15. Therefore, the selling price of the house was $172,815.15. The total interest paid can be calculated by subtracting the down payment amount from the future value: Total Interest Paid = Future Value - Down Payment = $172,815.15 - $36,655 = $136,160.15. Therefore, the total interest paid is $136,160.15.