Question

Round any decimals to the nearest penny.
You saved $10,943.89 in an emergency fund. One fourth is in a regular savings account at a 3.5% APR, and the remainder is in a 30-day CD at a 4.57% APR. What is the difference in the amount of interest earned in 30 days between the two savings instruments?
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Answer 1

To find the difference in the amount of interest earned in 30 days between the regular savings account and the 30-day CD, we will first need to determine the amounts in each account and then calculate the interest earned from each.

1. **Total Savings Amount:** $10,943.89

2. **Amount in Regular Savings Account:**
\[
\text{Amount in savings account} = \frac{1}{4} \times 10,943.89 = 2,735.97
\]

3. **Amount in 30-Day CD:**
\[
\text{Amount in CD} = 10,943.89 - 2,735.97 = 8,207.92
\]

4. **Interest Earned in Regular Savings Account:**
- APR = 3.5%
- Interest for 30 days (1 month) can be calculated as:
\[
\text{Interest} = \text{Principal} \times \left(\frac{\text{APR}}{12}\right)
\]
\[
\text{Interest in savings account} = 2,735.97 \times \left(\frac{0.035}{12}\right) = 2,735.97 \times 0.00291667 \approx 7.96
\]

5. **Interest Earned in 30-Day CD:**
- APR = 4.57%
- Interest for 30 days can be calculated similarly:
\[
\text{Interest in CD} = 8,207.92 \times \left(\frac{0.0457}{12}\right)
\]
\[
\text{Interest in CD} = 8,207.92 \times 0.00380833 \approx 31.29
\]

6. **Difference in Interest Earned:**
- Now we will find the difference between the interest earned in the CD and the interest earned in the savings account:
\[
\text{Difference} = \text{Interest in CD} - \text{Interest in savings account} = 31.29 - 7.96 = 23.33
\]

Thus, the difference in the amount of interest earned in 30 days between the two savings instruments is **$23.33**.