Question

anthony wants to buy a CD for $400 that earns 2.5% APR and is compounded quarterly. the CD matures in 3 years. he will be paid the interest he earns each quarter. how much interest will anthony have earned on this CD after the first quarter?

A. $1.25
B. $3.25
C. $2.50
D. $10.00

Answer 1

To calculate the interest Anthony will earn on his CD after the first quarter, we can follow these steps:

1. **Identify the variables**:
- Principal (P) = $400
- Annual Interest Rate (r) = 2.5% = 0.025
- Compounding periods per year (n) = 4 (quarterly)
- Time period in years (t) = 1 quarter = 1/4 years

2. **Calculate the interest for one quarter**:
The interest for one period can be calculated using the formula:
\[
\text{Interest} = P \times \left(\frac{r}{n}\right) \times t
\]
Plugging in the values:
\[
\text{Interest} = 400 \times \left(\frac{0.025}{4}\right) \times 1
\]

First, calculate \(\frac{0.025}{4}\):
\[
\frac{0.025}{4} = 0.00625
\]

Now plug this back into the formula for interest:
\[
\text{Interest} = 400 \times 0.00625 \times 1 = 2.50
\]

So, the interest Anthony will have earned on this CD after the first quarter is **$2.50**.

The correct answer is **C. $2.50**.