A principal of US$1600 is invested at 8,5% interest, compounded annually. How much will the investment be worth after 7 years?Use the calculator provided and round your answer to the nearest dollar.

To determine the future value of an investment with compound interest, we 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:

• $P = 1600$ USD
• $r = 8.5\% = 0.085$
• $n = 1$ (since the interest is compounded annually)
• $t = 7$ years

Substitute these values into the formula:

$A = 1600 \left(1 + \frac{0.085}{1}\right)^{1 \times 7}$

Simplify inside the parentheses:

$A = 1600 \left(1 + 0.085\right)^7$

$A = 1600 \left(1.085\right)^7$

Now, calculate $(1.085)^7$:

$(1.085)^7 \approx 1.747422$

Then multiply by the principal amount:

$A = 1600 \times 1.747422$

$A \approx 2795.88$

Rounding to the nearest dollar:

$A \approx 2796$

So, the investment will be worth approximately 2796 USD after 7 years.