Final answer:
To pay off the debt of $29,000 with a sinking fund at a 9% interest rate compounded semi-annually in 5 years, the company must deposit approximately $2,699.70 at the end of each half-year.
Step-by-step explanation:
To calculate the amount of money that needs to be deposited at the end of each half-year into a sinking fund, we need to use the formula for the future value of an ordinary annuity. The formula is:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
Where:
- FV is the future value (the debt of $29,000)
- P is the payment (what we need to find)
- r is the annual interest rate (9%)
- n is the number of periods per year (2 because it is compounded semi-annually)
- t is the number of years (5)
By substituting the values into the formula, we can solve for P:
$29,000 = P * [(1 + 0.09/2)^(2*5) - 1] / (0.09/2)
By evaluating the expression, we find that P is approximately $2,699.70.