Final answer:
The total in the Otwell Company's sinking fund after five years, with an annual contribution of $16,000 and an interest rate of 6.4% compounded annually, will be approximately $92,140 due to the power of compound interest.
Step-by-step explanation:
The question deals with a company's sinking fund, where a fixed amount is added annually, and the fund earns compound interest. To calculate the fund's balance after five years, the formula for the future value of a series of equal payments made at regular intervals, known as an ordinary annuity, can be used. The formula is: Future Value of Annuity (FV) = P × {[(1 + r)^n - 1] / r}, where P is the annual payment, r is the annual interest rate as a decimal, and n is the number of years.
In this scenario, P is $16,000, r is 6.4% or 0.064, and n is 5 years. Therefore, the calculation is:
FV = $16,000 × {[(1 + 0.064)^5 - 1] / 0.064}
Calculating this, we get:
FV = $16,000 × {[(1.064)^5 - 1] / 0.064}
= $16,000 × {[1.36856 - 1] / 0.064}
= $16,000 × 5.75875
= $92,140
The amount in the fund after five years will be approximately $92,140.
It's important to note that compound interest plays a significant role in the growth of investments over time. Even relatively small amounts can accumulate to substantial sums when you benefit from the power of compound interest over a longer period.