Question

You invest $75.00 the first month and $1,000.00 the second month at 3.75% APR. How much interest do you accrue at the end of the second month? (1 point) Responses $0.23 $0.23 $3.36 $3.36 $3.59 $3.59 $3.13

Answer 1

To calculate the interest accrued at the end of the second month on the amounts you invested, you can use the formula for simple interest:

\[ \text{Interest} = P \times r \times t \]

Where:
- \( P \) = principal amount (the amount of money invested)
- \( r \) = annual interest rate (as a decimal)
- \( t \) = time in years

1. **First Month Investment**:
- \( P_1 = 75.00 \)
- \( r = 3.75\% = 0.0375 \)
- For the first month, \( t_1 = \frac{1}{12} \) years

\[
\text{Interest for first month} = 75.00 \times 0.0375 \times \frac{1}{12}
\]

\[
\text{Interest for first month} = 75.00 \times 0.0375 \times 0.0833 = 0.234375
\]

2. **Second Month Investment** (including the first month's interest):
- First, calculate the interest on the first month's investment for the second month:

\[
\text{Interest for second month on first investment} = 75.00 \times 0.0375 \times \frac{1}{12} \quad (\text{same as above})
\]

\[
\text{Interest for second month on first investment} = 0.234375
\]

- Now calculate the interest on the second month investment:

- \( P_2 = 1000.00 \)
- For the second month, \( t_2 = \frac{1}{12} \) years

\[
\text{Interest for second month on second investment} = 1000.00 \times 0.0375 \times \frac{1}{12}
\]

\[
\text{Interest for second month on second investment} = 1000.00 \times 0.0375 \times 0.0833 = 3.125
\]

3. **Total Interest at the end of the second month**:

\[
\text{Total interest} = \text{Interest from first month} + \text{Interest from second month on first} + \text{Interest from second month on second}
\]

\[
\text{Total interest} = 0.234375 + 0.234375 + 3.125 \approx 3.59375
\]

Thus, rounding this calculation to two decimal points gives approximately **$3.59**.

The correct response from the options given is **$3.59**.