To find the total amount after 4 years of investment of S2000 at an interest rate of 3.1% compounded quarterly, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
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 interest is compounded per year.
- \(t\) is the number of years the money is invested for.
Given:
- \(P = 2000\)
- \(r = 3.1% = 0.031\)
- \(n = 4\) (since it is compounded quarterly)
- \(t = 4\)
Plugging in the values:
\[ A = 2000 \left(1 + \frac{0.031}{4}\right)^{4 \times 4} \]
Now, calculate the individual components:
- Calculate the quarterly interest rate:
\[ \frac{0.031}{4} = 0.00775 \]
- Calculate the total number of compounding periods:
\[ n \times t = 4 \times 4 = 16 \]
- Substitute these values back into the formula:
\[ A = 2000 \left(1 + 0.00775\right)^{16} \]
- Calculate \(1 + 0.00775\):
\[ 1 + 0.00775 = 1.00775 \]
- Raise this to the power of 16:
\[ 1.00775^{16} \approx 1.127304 \]
- Now multiply by the principal:
\[ A \approx 2000 \times 1.127304 \approx 2254.608 \]
- Finally, round the answer to the nearest cent:
\[ A \approx 2254.61 \]
Thus, the total amount after 4 years is $2254.61.