Question

Soyent Green ladscaping wants to build a $250,000 greenhouse in 3 years. The company sets up a sinking fund into which they plan to make equal payments at the end of each quarter in order to save the money needed to pay for the greenhouse. How much should they deposit at a minimum into this fund at the end of each quarter in order to achieve their goal of saving $250,000 in 3 years if the money in the fund earns 5% interest compunded quarterly?

A. 14,789.38 B. $19439.58 C. $18533.88 D. $20833.33 E. $20411.56

Answer 1

The Calculation of the quarterly payment amount to be made at the end of each quarter to achieve the goal of saving $250,000 in 3 Years

The quarterly payment is computed using the following formula:

Quarterly Payment = Total Accumulated Savings x [(Interest Rate/100) / {(1 + Interest Rate)ⁿ} – 1]

Where, Total Accumulated Savings = $250,000

r = 5% / 4 Quarters = 1.25% [Since, The Compounding is done quarterly]

n = 3 Years x 4 = 12 Periods [Since, The Compounding is done quarterly]

Then, Substitute the above data’s into the equation

Quarterly Payment = Total Accumulated Savings x [(Interest Rate/100) / {(1 + Interest Rate)ⁿ} – 1]

= $250,000 x [(1.0125) / {(1 + 0.125)ⁿ} – 1]

= $250,000 x [(1.0125) / (1.160754 – 1)]

= $250,000 x 0.077758

= $19,439.58

“Hence, The Answer is $19,439.58”