To determine which account will pay Maria more interest, we will calculate the future value of the inherited $7900 in both accounts after 1 year. We'll use the compound interest formula:

$A = P \left( 1 + \frac{r}{n} \right)^{nt}$

Where:

• $A$ is the amount of money accumulated after interest.
• $P$ is the principal amount (initial investment) = $7900.
• $r$ is the annual interest rate (as a decimal).
• $n$ is the number of times the interest is compounded per year.
• $t$ is the time the money is invested for (in years).

Account 1 (compounded semi-annually):

• $P = 7900$
• $r = 5.1\% = 0.051$
• $n = 2$ (semi-annually)
• $t = 1$ year

$A_1 = 7900 \left( 1 + \frac{0.051}{2} \right)^{2 \cdot 1}$

Account 2 (compounded annually):

• $P = 7900$
• $r = 4.7\% = 0.047$
• $n = 1$ (annually)
• $t = 1$ year

$A_2 = 7900 \left( 1 + \frac{0.047}{1} \right)^{1 \cdot 1}$

Let's calculate the future values for both accounts to determine which one pays more interest.### Future Values:

• Account 1 (compounded semi-annually): $8308.04
• Account 2 (compounded annually): $8271.30

Interest Earned:

• Account 1: $408.04
• Account 2: $371.30

Thus, Account 1 pays Maria more interest, with a difference of approximately $36.74.

Would you like to see more details on this calculation, or do you have any questions?

Here are 5 related questions you might find useful:

1. What happens if Maria deposits her money for 5 years?
2. How does monthly compounding compare to semi-annual compounding?
3. What if Maria deposits an additional $1000 after 6 months?
4. How would a different initial amount (e.g., $5000) affect the interest earned?
5. What is the formula for continuous compounding, and how would it compare?

Tip: Compounding more frequently generally results in more interest earned.