Question

A sinking fund is established to discharge a debt of $20,000 in 15 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 5%, compounded semiannually, what is the amount of each deposit? (Round your answer to the nearest cent.)

Answer 1

Answer:

the amount of each deposit is $45,555

Step-by-step explanation:

The computation of the each deposit is shown below:

Given that

Future value be $20,000

Time period = 15 × 2 = 30

And, the rate = 5% ÷ 2 = 2.5%

Now the formula is as follows

= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1

= ($20,000 × 2.5) ÷ (1 + 0.025)^30 - 1

= $50,000 ÷ 1.0975675791

= $45,555

Hence, the amount of each deposit is $45,555