Final answer:
To identify which investment option yields a greater return, we compute the future value of $4,000 invested at 7.92% compounded daily and 8.0% compounded quarterly over 10 years using the compound interest formula and then compare the results.
Step-by-step explanation:
To determine which investment yields the greater return over a 10-year period, we compare the results of compound interest for both the 7.92% compounded daily and the 8.0% compounded quarterly.
Using the compound interest formula 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.
For the 7.92% compounded daily option (n = 365):
A = $4,000(1 + 0.0792/365)^(365*10)
For the 8.0% compounded quarterly option (n = 4):
A = $4,000(1 + 0.08/4)^(4*10)
To find the greater return, we calculate the final amounts for both cases and compare them.