Suppose that US$2000 is invested at an annual interest rate of 4,7%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 7 years.

To find the total amount after 7 years for an investment of US$2000 at an annual interest rate of 4.7%, compounded quarterly, follow these steps:

1. Identify the principal amount (P): $P = 2000$ USD

2. Determine the annual interest rate (r): $r = 4.7\% = 0.047$

3. Determine the number of times interest is compounded per year (n): Since the interest is compounded quarterly, $n = 4$

4. Determine the number of years the money is invested (t): $t = 7$ years

5. Use the compound interest formula: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ where $A$ is the amount of money accumulated after n years, including interest.

6. Substitute the values into the formula: $A = 2000 \left(1 + \frac{0.047}{4}\right)^{4 \times 7}$

7. Calculate the value inside the parentheses: $1 + \frac{0.047}{4} = 1 + 0.01175 = 1.01175$

8. Calculate the exponent: $4 \times 7 = 28$

9. Raise the base to the power of the exponent: $1.01175^{28} \approx 1.349858$

10. Multiply by the principal amount: $A = 2000 \times 1.349858 \approx 2699.72$

Therefore, the total amount after 7 years is approximately US$2699.72.