The Davidson's have a lump sum amount of $60,000 saved up and have the budget to pay $2,500 at the start of each month for mortgage payments over 25 years. Determine the price of the home they can afford given interest rates are at 5.95% compounded monthly.

Question

Quizplus · Accepted Answer

The price of the home the Davidson's can afford can be calculated using the formula for the present value of an annuity to account for the monthly payments, plus the lump sum amount they already have. Given an interest rate of 5.95% per annum compounded monthly, this translates to a monthly interest rate of $5.95\% / 12 = 0.49583\%$. Over 25 years, or 300 months, they can afford a home priced at the sum of the present value of their monthly payments and their initial savings. The formula for the present value of an annuity is $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $P$ is the payment amount, $r$ is the monthly interest rate in decimal form, and $n$ is the total number of payments. Substituting $P = 2500$, $r = 0.0049583$, and $n = 300$, we find the present value of the annuity. Adding the lump sum of $60,000 to this gives the total price of the home they can afford. The correct calculation leads to a total that falls closest to option B, $451,798, when properly computed.

The Davidson's Have a Lump Sum Amount of $60,000 Saved