Final answer:
The claim that $1,864 should be used as the present value is false; $1,864 represents the future value of the initial investment. To calculate the time taken for the investment to reach this amount, the compound interest formula would be used, taking into account the initial investment amount, the interest rate, and the compounding frequency.
Step-by-step explanation:
The statement that when computing the number of years, the $1,864 should be used as the present value is False. When you are trying to determine the number of years it takes for an investment to grow to a certain amount, you use the future value of the investment, not the present value. In this case, the $1,864 is the future value of the initial $500 investment.
To solve for the number of years, a common approach is to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
However, if the interest is compounded only once per year, the formula simplifies to A = P(1 + r)^t. Without additional information regarding compounding frequency, we would use this simpler formula and rearrange it to solve for t, which represents the number of years.