Final answer:
Using the compound interest formula, an investment of $10,000 at a 10% return rate annually will be worth approximately $16,105.10 after five years, which is nearly true to the claim of $16,110.
Step-by-step explanation:
To determine whether it is true that an investment of $10,000 in a good mutual fund that pays an average 10% return will be worth $16,110 five years from now, we can use the formula for compound interest which is A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, if the interest is compounded annually (n=1), the formula simplifies to A = P(1 + r)^t. Plugging in the values, we get A = 10,000(1 + 0.10)^5 = 10,000(1.10)^5. Calculating the power of 1.10^5 gives us approximately 1.61051, so the investment will be worth approximately 10,000 * 1.61051 = $16,105.10 after five years. Therefore, the statement is almost true, with a small discrepancy possibly due to rounding during the calculation.