The problem describes a sinking fund established to pay off a debt of $60,000 in 15 years. Deposits are made at the end of each 6-month period, and the interest rate is 6% compounded semiannually. We need to calculate the amount of each deposit.

1. Problem Description

The problem describes a sinking fund established to pay off a debt of $60,000 in 15 years. Deposits are made at the end of each 6-month period, and the interest rate is 6% compounded semiannually. We need to calculate the amount of each deposit.

2. Solution Steps

The formula for the periodic payment $P$ required to accumulate a future value $FV$ with regular deposits is:

$P = \frac{FV \cdot i}{(1+i)^n - 1}$

Where:

$FV$ = Future Value = $60,000

$i$ = interest rate per period = $\frac{6\%}{2} = 0.03$

$n$ = number of periods = $15 \text{ years} \times 2 = 30$

Plug in the values:

$P = \frac{60000 \times 0.03}{(1+0.03)^{30} - 1}$

$P = \frac{1800}{(1.03)^{30} - 1}$

$P = \frac{1800}{2.42726247 - 1}$

$P = \frac{1800}{1.42726247}$

$P = 1261.135$

Round to the nearest cent:

$P = 1261.14$

3. Final Answer

The amount of each deposit is $1261.14.