Beatrice invests $1,450 in an account that pays 4 percent simple interest. How much more could she have earned over a 5-year period if the interest had been compounded annually?

Multiple Choice

$120.73


$28.12


$20.32


$24.15


$35.16

To determine how much more Beatrice could have earned with compound interest instead of simple interest, we'll calculate both and find the difference. 

### Step 1: Calculate the simple interest earned.

The formula for simple interest is:

\[
I = P \times r \times t
\]

Where:
- $ P = 1450 $ (principal),
- $ r = 0.04 $ (interest rate per year),
- $ t = 5 $ (time in years).

\[
I = 1450 \times 0.04 \times 5 = 290
\]

So, Beatrice would have earned **$290** in simple interest over 5 years.

### Step 2: Calculate the compound interest earned.

The formula for compound interest is:

\[
A = P \times (1 + \frac{r}{n})^{n \times t}
\]

Where:
- $ P = 1450 $,
- $ r = 0.04 $,
- $ n = 1 $ (since the interest is compounded annually),
- $ t = 5 $.

\[
A = 1450 \times \left(1 + \frac{0.04}{1}\right)^{1 \times 5}
\]
\[
A = 1450 \times (1.04)^5 \approx 1450 \times 1.216653 \approx 1764.14
\]

The total amount with compound interest is **$1764.14**. Therefore, the compound interest earned is:

\[
1764.14 - 1450 = 314.14
\]

### Step 3: Find the difference between compound interest and simple interest.

\[
314.14 - 290 = 24.14
\]

Thus, Beatrice could have earned approximately **$24.14** more with compound interest. Since the closest option is **$24.15**, the correct answer is:

**$24.15**

Would you like a more detailed explanation of any part of this calculation?

Here are 5 related questions to think about:
1. How would the outcome change if the interest were compounded monthly instead of annually?
2. What would the interest be after 10 years with the same annual compounding rate?
3. What if Beatrice invested $2,000 at the same interest rates? How would the difference change?
4. How does the frequency of compounding affect the total interest earned?
5. What would happen if the simple interest rate were higher than the compound interest rate?

**Tip:** Compounding more frequently (monthly, daily, etc.) results in greater interest compared to compounding annually or simple interest.

Beatrice invests $1,450 in an account that pays 4 percent simple interest. How much more could she have earned over a 5-year period if the interest had been compounded annually? Multiple Choice: $120.73, $28.12, $20.32, $24.15, $35.16

Discover how much more Beatrice could have earned with compound interest instead of simple interest on her $1,450 investment over 5 years at a 4% interest rate. This problem covers the calculation of both simple and compound interest, highlighting the difference of $24.15 between the two. Suitable for students in Grades 9-12.

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