Question

Abdul invests $5,000 at an interest
rate of 4%, compounded quarterly.
How much is the investment worth
at the end of 3 years?
𝖠 $624.32
𝖡 $5624.32
𝖢 $634.13
𝖣 $5634.13

Answer 1

To calculate the future value of an investment with compound interest, we can use the formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.

Given:
- \( P = 5000 \)
- \( r = 0.04 \) (4% expressed as a decimal)
- \( n = 4 \) (because it is compounded quarterly)
- \( t = 3 \)

Now, plugging these values into the formula:

\[
A = 5000 \left(1 + \frac{0.04}{4}\right)^{4 \cdot 3}
\]

Calculating step by step:

1. Calculate \(\frac{r}{n}\):
\[
\frac{0.04}{4} = 0.01
\]

2. Thus, we have:
\[
A = 5000 \left(1 + 0.01\right)^{12}
\]

3. Calculate \((1 + 0.01)^{12}\):
\[
1.01^{12} \approx 1.12749
\]

4. Now substitute back into the formula:
\[
A \approx 5000 \times 1.12749 \approx 5637.45
\]

So, the investment is worth approximately \(5637.45\). Considering the answer choices, the closest answer would be:

\[
\text{D: } \$5634.13
\]

Therefore, the answer is **𝖣 $5634.13**.