Suppose that US$2000 is loaned at an annual rate of 6,5%, compounded quarterly. Assuming that no payments are made, find the amount owed after 7 years.Do not round any intermediate computations, and round your answer to the nearest cent.

To find the amount owed after 7 years for a loan of US$2000 at an annual interest rate of 6.5%, compounded quarterly, we can 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.
• $P$ is the principal amount (the initial amount of money, which is US$2000).
• $r$ is the annual interest rate (decimal), which is 6.5% or 0.065.
• $n$ is the number of times that interest is compounded per year (quarterly, so $n = 4$).
• $t$ is the time the money is invested for in years (7 years).

Now, plug in the values:

$A = 2000 \left(1 + \frac{0.065}{4}\right)^{4 \times 7}$

First, calculate the quarterly interest rate:

$\frac{0.065}{4} = 0.01625$

Next, calculate the exponent:

$4 \times 7 = 28$

Now, calculate the base of the exponent:

$1 + 0.01625 = 1.01625$

Raise this to the power of 28:

$1.01625^{28} \approx 1.563281$

Finally, multiply this by the principal amount:

$A = 2000 \times 1.563281 \approx 3126.56$

So, the amount owed after 7 years is approximately US$3126.56.