Final answer:
The investment with 1.3% compounded continuously yields a greater return over 7 years compared to the investment with 1.2% compounded monthly.
Step-by-step explanation:
To determine which investment yields the greater return over 7 years, let's compare the two options: 1.2% compounded monthly and 1.3% compounded continuously.
For the 1.2% compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal amount, r is the interest rate per compounding period, n is the number of compounding periods per year, and t is the number of years.
Plugging the values into the formula:
A = 25000(1 + 0.012/12)^(12*7) = 28392.71
So, the 1.2% compounded monthly yields a final amount of $28,392.71
For the 1.3% compounded continuously, we can use the formula:
A = Pe^(rt)
Where e is Euler's number approximately equal to 2.71828.
Plugging the values into the formula:
A = 25000e^(0.013*7) = 28401.52
So, the 1.3% compounded continuously yields a final amount of $28,401.52
Therefore, the investment with 1.3% compounded continuously yields a greater return over 7 years.