Final answer:
Using the compound interest formula, it would take approximately 11.89 years for an investment of $657.00 to grow to $2,821.00 at an annual rate of return of 14.09%.
Step-by-step explanation:
To calculate how many years it would take for an investment of $657.00 to grow to $2,821.00 at an annual rate of return of 14.09%, we can 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 (the initial amount of money).
- 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.
Since the question doesn't specify how often the interest is compounded, we'll assume it's compounded annually (n=1). Therefore, the equation simplifies to A = P(1 + r)t. Rearrange the equation to solve for t: t = ln(A/P) / ln(1 + r)
Plugging in the given values: t = ln(2,821 / 657) / ln(1 + 0.1409)
Now, you would calculate the value using a calculator: t = ln(4.29376) / ln(1.1409)
After doing the math: t ≈ 11.89
It would take approximately 11.89 years for the investment to grow from $657.00 to $2,821.00 at a 14.09% annual rate of return.