Solve the application problem. Round to the nearest cent.
-Green Thumb Landscaping wants to build a $129,000 greenhouse in 2 years. The company sets up a sinking fund with payments made quarterly. Find the payment into this fund if the money earns 8% compounded quarterly.

Question

Solve the application problem. Round to the nearest cent. 
-Green Thumb Landscaping wants to build a $129,000 greenhouse in 2 years. The company sets up a sinking fund with payments made quarterly. Find the payment into this fund if the money earns 8% compounded quarterly.

Quizplus · Accepted Answer

To find the quarterly payment for a sinking fund, we use the formula for the future value of an annuity: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value, $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Here, $FV = \$129,000$, the annual interest rate is 8% (or 0.08), which when compounded quarterly gives $r = 0.08/4 = 0.02$ (2% per quarter), and with payments made quarterly for 2 years, $n = 2 \times 4 = 8$ quarters. Rearranging the formula to solve for $P$, we get $P = FV \times \frac{r}{(1 + r)^n - 1}$. Substituting the given values, we get $P = 129,000 \times \frac{0.02}{(1 + 0.02)^8 - 1}$, which calculates to approximately \$15,029.79.

Solve the Application Problem