Question
Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45-day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days? Round to the nearest penny.
Answers
GPT-4o mini
To determine the total interest earned in 45 days from the investments, we will first calculate the amount of investment in each account, then calculate the interest earned from both the savings account and the certificate of deposit (CD).
1. **Calculate the amount invested in each account:**
Your fixed expenses are $1,500.45/month, and you have an emergency fund covering 4 months. Therefore, the total emergency fund amount is:
\[
\text{Total Emergency Fund} = 1,500.45 \times 4 = 6,001.80
\]
You invest half in a savings account and half in a 45-day CD:
\[
\text{Amount in Savings Account} = \frac{6,001.80}{2} = 3,000.90
\]
\[
\text{Amount in CD} = \frac{6,001.80}{2} = 3,000.90
\]
2. **Calculate the interest from the savings account after 45 days:**
The annual interest rate for the savings account is 3.15% APR. To find the interest for 45 days, we need to convert this annual rate into a daily rate:
\[
\text{Daily Interest Rate} = \frac{3.15\%}{365} = \frac{0.0315}{365} \approx 0.0000862337
\]
Next, we calculate the interest for 45 days:
\[
\text{Interest in Savings} = \text{Amount in Savings} \times \text{Daily Interest Rate} \times 45
\]
\[
= 3,000.90 \times 0.0000862337 \times 45 \approx 3,000.90 \times 0.0038665115 \approx 11.61
\]
3. **Calculate the interest from the CD after 45 days:**
The interest rate for the CD is 4.65% APR. Similarly, convert this to a daily rate:
\[
\text{Daily Interest Rate for CD} = \frac{4.65\%}{365} = \frac{0.0465}{365} \approx 0.00012739726
\]
Then, calculate the interest for 45 days:
\[
\text{Interest in CD} = \text{Amount in CD} \times \text{Daily Interest Rate for CD} \times 45
\]
\[
= 3,000.90 \times 0.00012739726 \times 45 \approx 3,000.90 \times 0.0057338747 \approx 17.17
\]
4. **Calculate the total interest earned:**
\[
\text{Total Interest} = \text{Interest in Savings} + \text{Interest in CD}
\]
\[
= 11.61 + 17.17 \approx 28.78
\]
Therefore, the total interest earned in 45 days is approximately **$28.78**.
1. **Calculate the amount invested in each account:**
Your fixed expenses are $1,500.45/month, and you have an emergency fund covering 4 months. Therefore, the total emergency fund amount is:
\[
\text{Total Emergency Fund} = 1,500.45 \times 4 = 6,001.80
\]
You invest half in a savings account and half in a 45-day CD:
\[
\text{Amount in Savings Account} = \frac{6,001.80}{2} = 3,000.90
\]
\[
\text{Amount in CD} = \frac{6,001.80}{2} = 3,000.90
\]
2. **Calculate the interest from the savings account after 45 days:**
The annual interest rate for the savings account is 3.15% APR. To find the interest for 45 days, we need to convert this annual rate into a daily rate:
\[
\text{Daily Interest Rate} = \frac{3.15\%}{365} = \frac{0.0315}{365} \approx 0.0000862337
\]
Next, we calculate the interest for 45 days:
\[
\text{Interest in Savings} = \text{Amount in Savings} \times \text{Daily Interest Rate} \times 45
\]
\[
= 3,000.90 \times 0.0000862337 \times 45 \approx 3,000.90 \times 0.0038665115 \approx 11.61
\]
3. **Calculate the interest from the CD after 45 days:**
The interest rate for the CD is 4.65% APR. Similarly, convert this to a daily rate:
\[
\text{Daily Interest Rate for CD} = \frac{4.65\%}{365} = \frac{0.0465}{365} \approx 0.00012739726
\]
Then, calculate the interest for 45 days:
\[
\text{Interest in CD} = \text{Amount in CD} \times \text{Daily Interest Rate for CD} \times 45
\]
\[
= 3,000.90 \times 0.00012739726 \times 45 \approx 3,000.90 \times 0.0057338747 \approx 17.17
\]
4. **Calculate the total interest earned:**
\[
\text{Total Interest} = \text{Interest in Savings} + \text{Interest in CD}
\]
\[
= 11.61 + 17.17 \approx 28.78
\]
Therefore, the total interest earned in 45 days is approximately **$28.78**.