Second Hand Software needs to accumulate \( \$ 12,000 \) in 3 years to meet future needs. What sinking fund payment would they need to make at the end of each year, at \( 6 \% \) interest compounded annually? Select one: a. \( \$ 4,110.34 \) b. \( \$ 3,769.32 \) c. \( \$ 4,392.65 \) d. \( \$ 4,634.15 \)
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Bonus Knowledge
To find the sinking fund payment needed to accumulate \( \$ 12,000 \) in 3 years at an interest rate of \( 6\% \) compounded annually, you can use the formula for the future value of a sinking fund: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value (\$12,000) - \( P \) is the annual payment (sinking fund payment) - \( r \) is the interest rate per period (0.06) - \( n \) is the number of periods (3) Rearranging the formula to solve for \( P \): \[ P = \frac{FV \times r}{(1 + r)^n - 1} \] Substituting in the values: \[ P = \frac{12000 \times 0.06}{(1 + 0.06)^3 - 1} = \frac{720}{1.191016 - 1} = \frac{720}{0.191016} = 3,769.32 \] Thus, the correct sinking fund payment is b. \( \$ 3,769.32 \).
