Final answer:
The amount in the Otwell Company's sinking fund after 5 years is calculated by using a formula for compound interest, specifically designed for recurring investments, known as a future value of an annuity formula. The exact value requires numerical computation based on the sum of compound interest for each $16,000 annual investment.
Step-by-step explanation:
The Otwell Company is using a sinking fund to save for major equipment purchases. To determine the amount in the sinking fund after 5 years, we use the formula for compound interest:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($16,000 per year).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, since interest is compounded annually (n=1) and the interest rate is 6.4%, the calculation with an annual $16,000 addition is a bit more complex than a single principal amount. This requires us to calculate each year's investment and its compound interest separately then sum them up.
Therefore, by calculating the compound interest for each $16,000 invested annually over 5 years, we can find the total. However, as the details on how the payments are made into the fund are not provided (e.g., beginning or end of the year), a general formula for a future value of an annuity would be more appropriate:
FV = P × { [(1 + r)n - 1] / r }
Applying the given figures:
FV = $16,000 × { [(1 + 0.064)5 - 1] / 0.064 }
The future value after 5 years, derived from this compound interest annuity formula, would be the final answer, rounded to two decimal places as per instruction.