Lowell Corporation wishes to establish a sinking fund to retire a $210,000 debt that is due in 12 years. If the investment will earn interest at the rate of 10%/year compounded quarterly, find the amount of the quarterly deposit that must be made in order to accumulate the required sum. Round your answer to the nearest cent.
A) R = $2,348.74
B) R = $2,311.26
C) R = $2,287.73
D) R = $2,368.61

Question

Lowell Corporation wishes to establish a sinking fund to retire a $210,000 debt that is due in 12 years. If the investment will earn interest at the rate of 10%/year compounded quarterly, find the amount of the quarterly deposit that must be made in order to accumulate the required sum. Round your answer to the nearest cent. ​
A) R = $2,348.74
B) R = $2,311.26
C) R = $2,287.73
D) R = $2,368.61

Quizplus · Accepted Answer

To find the quarterly deposit (R) needed to accumulate a future sum (FV) of $210,000 in 12 years with an interest rate of 10% per year compounded quarterly, we use the future value of an annuity formula: $FV = R \times \frac{(1 + r)^n - 1}{r}$, where $r$ is the quarterly interest rate and $n$ is the total number of deposits. Here, $r = \frac{10\%}{4} = 0.025$ (2.5% per quarter), and $n = 12 \times 4 = 48$ quarters. Rearranging the formula to solve for R gives us $R = FV \times \frac{r}{(1 + r)^n - 1}$. Plugging in the values, we get $R = 210,000 \times \frac{0.025}{(1 + 0.025)^{48} - 1}$, which calculates to approximately $2,311.26.

Lowell Corporation Wishes to Establish a Sinking Fund to Retire