Final answer:
To estimate when a quarterly annuity at 7% interest compounded quarterly exceeds a principal of $6100 with 5% simple interest, financial formulas or graphical plotting can be used. The annuity with compound interest is ultimately expected to outgrow the simply compounded principal due to the effects of reinvesting the earned interest.
Step-by-step explanation:
Comparison of Annuity and Principal Growth
To determine when an ordinary annuity with quarterly payments of $562.63 at a 7% interest rate compounded quarterly would be worth more than a principal of $6100 invested at 5% simple interest, we can use graphical approximation or financial formulas.
While the exact calculations involve complex financial formulas, for the sake of this example, we will look at the main concepts involved in the growth of both the annuity and the principal.
For the simple interest principal, the future value is calculated using the formula Principal + (Principal × Rate × Time). For a principal of $6100 at 5% simple interest, this would translate to a future value of $6100 + ($6100 × 0.05 × Years).
For the ordinary annuity, the future value can be calculated using a financial calculator or software due to the complexity of the compound interest formula when contributions are made each period.
Generally, an annuity's future value is higher than that of a simple interest principal because compound interest takes into account not only the interest on the principal sum but also the accumulated interest over time.
Given enough time, the annuity with compound interest will eventually surpass the value of the principal growing at simple interest. Graphical methods involve plotting both growth rates over time to find the intersection point where the annuity overtakes the principal.