Final answer:
It will take approximately 27.9 years for a $5,000 ordinary annuity to reach a value of $100,000 at a 5% annual interest rate. There isn't a straightforward algebraic approach to solve for time, but financial tables or calculators can provide the answer.
Step-by-step explanation:
To determine how long it will take for a $5,000 ordinary annuity to grow to $100,000 at a 5% annual interest rate, we need to use the formula for the future value of an ordinary annuity. Unfortunately, there isn't a simple algebraic formula to directly solve for time in the annuity formula; it requires either iterative methods or financial calculators. However, we can refer to financial tables or use a financial calculator to find that the amount of time it takes to grow an annuity from $5,000 to $100,000 at 5% interest is closest to the option c. 27.9 years.
To determine the time required for a $5,000 ordinary annuity to grow to $100,000 at a 5% annual interest rate, the future value of an ordinary annuity formula is employed. Unfortunately, solving for time in this formula involves iterative methods or financial calculators due to its complex nature. In lieu of direct algebraic solutions, financial tables or calculators are commonly used.
Upon referencing financial tables or using a financial calculator, the closest approximation for the time required to grow the annuity from $5,000 to $100,000 at a 5% interest rate is option C: 27.9 years. This calculation aids in understanding the gradual accumulation of value within an annuity over time, demonstrating the impact of interest rates on the growth of such financial instruments.