Maria has recently inherited $7900, which she wants to deposit into a savings account.  She has determined that her two best bets are an account that compounds semi-annually at an annual rate of 5.1% (Account 1) and an account that compounds annually at an annual rate of 4.7% (Account 2).

**Step 1 of 2 :**  

Which account would pay Maria more interest?





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.

Maria has recently inherited $7900, which she wants to deposit into a savings account. She has determined that her two best bets are an account that compounds semi-annually at an annual rate of 5.1% (Account 1) and an account that compounds annually at an annual rate of 4.7% (Account 2). Which account would pay Maria more interest?

Discover how to compare two savings accounts using the compound interest formula. In this example, Maria invests $7900, and we calculate the future value for semi-annual compounding at 5.1% and annual compounding at 4.7%. Suitable for students in Grades 10-12, learn how frequent compounding impacts interest earnings.

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