Fatima pays monthly rent of $520 for her townhouse. If she bought the property, the mortgage loan, property tax and utilities would cost her $920 per month. Using the current mortgage loan rate of 6.6% compounded semiannually, calculate how much money Fatima could accumulate over 10 years if she continues to rent and invests the $400 per month difference.

Question

Quizplus · Accepted Answer

Fatima can save $400 per month by continuing to rent. If she invests this amount at an interest rate of 6.6% compounded semiannually, over 10 years, the future value of this annuity can be calculated using the formula for the future value of an annuity: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. The annual interest rate is 6.6%, so the semiannual rate is 3.3%, and the monthly rate is $3.3\% / 6 = 0.55\%$, or 0.0055 in decimal form. The number of payments over 10 years is $10 \times 12 = 120$. Plugging these values into the formula gives the future value of Fatima's investment as approximately $67,768, making choice B correct.

Fatima Pays Monthly Rent of $520 for Her Townhouse