Suppose that $2000 is loaned at a rate of 9%, compounded semiannually. Assuming that no payments are made, find the amount owed after 6 years.

6 years is 12 compounds at 4.5 % each

2000 ( 1.045)^12

To find the amount owed after 6 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money accumulated after the time period
P = the principal amount (initial loan amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

In this case:
P = $2000
r = 9% = 0.09 (converted to decimal)
n = 2 (semiannual compounding)
t = 6 years

Substituting these values into the formula, we get:

A = 2000(1 + 0.09/2)^(2*6)

Now we can calculate the amount owed after 6 years.