Keith bought a lakeside cottage for 30% down and monthly mortgage payments of $1224.51 at the beginning of each month for 20 years. Interest is 4.4% compounded monthly. What is the purchase price of the property?

Question

Quizplus · Accepted Answer

The purchase price can be calculated using the formula for the present value of an annuity because the mortgage payments are fixed and made at regular intervals. The formula is $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where $PV$ is the present value (or loan amount), $PMT$ is the monthly payment, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (months). Given that the down payment was 30%, the loan amount represents 70% of the purchase price. First, calculate the loan amount using the given monthly payment, interest rate, and period:- $PMT = \$1224.51$- Annual interest rate = 4.4%, so monthly interest rate $r = \frac{4.4\%}{12} = 0.0036667$- $n = 20 \times 12 = 240$ monthsPlugging these into the formula gives the loan amount. Then, divide the loan amount by 0.7 to find the full purchase price, which matches option E, $279,900. This calculation confirms that the purchase price of the property is indeed $279,900, after accounting for the 30% down payment and the details of the mortgage.

Keith Bought a Lakeside Cottage for 30% Down and Monthly