Final answer:
The rate of return on a $50,000 investment guaranteeing an annuity of $10,489 for six years likely falls between 5% and 7%, without exact details it's not possible to specify the precise rate. Options A) 5% and C) 7% are viable, with option C) being a typical rate for such investments. The scenario is analogous to the compound interest concept illustrated by investing at a 10% or 7% rate to accumulate significant funds over time.
Step-by-step explanation:
The question concerns the calculation of the rate of return on an investment that guarantees a series of payments, which is a typical problem in the field of finance and particularly involves understanding annuities. To find the rate of return on a $50,000 investment that guarantees an annuity of $10,489 for six years, one would typically use the formula for the present value of an annuity or a financial calculator. However, since specific details of the payment frequency and the type of annuity (e.g., ordinary annuity or annuity due) are not provided, we're unable to give an exact percentage rate. But, by comparison to common financial scenarios, an approximate annual rate of return would likely be between 5% and 7%, putting options A) and C) as viable, with option C) coming close to typical rates for such an investment.
To further illustrate the concept, if you were to invest in a bank account with a 10% interest rate compounded annually to have $10,000 in ten years, you would use the formula for compound interest. Similarly, when investing $3,000 at a 7% real annual rate of return, compounded annually, this amount would grow significantly over time, demonstrating the power of compound interest.