You wish to have $25,000 on September 1,2012 to buy a new car.What monthly deposit is needed to achieve your goal if you can earn j₁₂ = 5.4% and you make monthly deposits from October 1,2007 to September 1,2012?

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. The annual interest rate is 5.4%, so the monthly interest rate is $5.4\% / 12 = 0.45\%$, or $0.0045$ in decimal form. The total number of payments from October 1, 2007, to September 1, 2012, is 5 years or 60 months. Plugging these values into the formula and solving for $P$ gives us the monthly deposit needed to reach $25,000 by September 1, 2012.

You Wish to Have $25,000 on September 1,2012 to Buy