Question
Round any decimals to the nearest penny.
Your fixed expenses are $1,328.90/month and you saved 4 months' worth in an emergency fund. You place half in a 45-day CD at a 4.5% APR and the remainder in a regular savings account at a 3.2% APR. How much total interest do you earn in 45 days?
$
Your fixed expenses are $1,328.90/month and you saved 4 months' worth in an emergency fund. You place half in a 45-day CD at a 4.5% APR and the remainder in a regular savings account at a 3.2% APR. How much total interest do you earn in 45 days?
$
Answers
GPT-4o mini
To calculate the total interest earned in 45 days, let's break this down step-by-step.
1. **Calculate the total amount in the emergency fund**:
\[
\text{Total savings} = \text{Fixed expenses} \times \text{Number of months saved}
\]
\[
\text{Total savings} = 1,328.90 \times 4 = 5,315.60
\]
2. **Divide the total savings into two parts**:
- Half in a 45-day CD:
\[
\text{Amount in CD} = \frac{5,315.60}{2} = 2,657.80
\]
- The remainder in a regular savings account:
\[
\text{Amount in savings account} = \frac{5,315.60}{2} = 2,657.80
\]
3. **Calculate the interest earned on the 45-day CD at 4.5% APR**:
- First, convert the APR into a daily interest rate:
\[
\text{Daily interest rate} = \frac{4.5\%}{365} \approx \frac{0.045}{365} \approx 0.00012328767
\]
- Then calculate the interest for 45 days:
\[
\text{Interest from CD} = \text{Amount in CD} \times \text{Daily interest rate} \times 45
\]
\[
\text{Interest from CD} = 2,657.80 \times 0.00012328767 \times 45 \approx 2,657.80 \times 0.005559952 \approx 14.75
\]
4. **Calculate the interest earned on the regular savings account at 3.2% APR**:
- First, convert the APR into a daily interest rate:
\[
\text{Daily interest rate} = \frac{3.2\%}{365} \approx \frac{0.032}{365} \approx 0.0000876712
\]
- Then calculate the interest for 45 days:
\[
\text{Interest from savings account} = \text{Amount in savings account} \times \text{Daily interest rate} \times 45
\]
\[
\text{Interest from savings account} = 2,657.80 \times 0.0000876712 \times 45 \approx 2,657.80 \times 0.003948204 \approx 10.48
\]
5. **Total interest earned**:
\[
\text{Total interest} = \text{Interest from CD} + \text{Interest from savings account}
\]
\[
\text{Total interest} = 14.75 + 10.48 = 25.23
\]
Thus, the total interest earned in 45 days is **$25.23**.
1. **Calculate the total amount in the emergency fund**:
\[
\text{Total savings} = \text{Fixed expenses} \times \text{Number of months saved}
\]
\[
\text{Total savings} = 1,328.90 \times 4 = 5,315.60
\]
2. **Divide the total savings into two parts**:
- Half in a 45-day CD:
\[
\text{Amount in CD} = \frac{5,315.60}{2} = 2,657.80
\]
- The remainder in a regular savings account:
\[
\text{Amount in savings account} = \frac{5,315.60}{2} = 2,657.80
\]
3. **Calculate the interest earned on the 45-day CD at 4.5% APR**:
- First, convert the APR into a daily interest rate:
\[
\text{Daily interest rate} = \frac{4.5\%}{365} \approx \frac{0.045}{365} \approx 0.00012328767
\]
- Then calculate the interest for 45 days:
\[
\text{Interest from CD} = \text{Amount in CD} \times \text{Daily interest rate} \times 45
\]
\[
\text{Interest from CD} = 2,657.80 \times 0.00012328767 \times 45 \approx 2,657.80 \times 0.005559952 \approx 14.75
\]
4. **Calculate the interest earned on the regular savings account at 3.2% APR**:
- First, convert the APR into a daily interest rate:
\[
\text{Daily interest rate} = \frac{3.2\%}{365} \approx \frac{0.032}{365} \approx 0.0000876712
\]
- Then calculate the interest for 45 days:
\[
\text{Interest from savings account} = \text{Amount in savings account} \times \text{Daily interest rate} \times 45
\]
\[
\text{Interest from savings account} = 2,657.80 \times 0.0000876712 \times 45 \approx 2,657.80 \times 0.003948204 \approx 10.48
\]
5. **Total interest earned**:
\[
\text{Total interest} = \text{Interest from CD} + \text{Interest from savings account}
\]
\[
\text{Total interest} = 14.75 + 10.48 = 25.23
\]
Thus, the total interest earned in 45 days is **$25.23**.