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Knowledge Check Question 2 uppose that $2000 is loaned at a rate of 9.5%, compounded semiannually. Assuming that no payments are made, find the amount owed after 7 years. o not round any intermediate computations, and round your answer to the nearest cent.

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Final answer:

The amount owed after 7 years on a $2000 loan with a 9.5% interest rate compounded semiannually would be $3895.25, rounded to the nearest cent.

Step-by-step explanation:

In response to Knowledge Check Question 2 regarding the compounding interest of a loan: To find the amount owed after 7 years on a $2000 loan at a rate of 9.5%, compounded semiannually, we use the formula for compound interest A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest, P is the principal amount ($2000), r is the annual interest rate (9.5% or 0.095), n is the number of times that interest is compounded per year (2 for semiannually), and t is the time the money is invested for, in years (7).

Calculating this out:

A = $2000(1 + 0.095/2)^(2 * 7)

A = $2000(1 + 0.0475)^(14)

A = $2000(1.0475)^(14)

A = $2000 * 1.9476229

A = $3895.25

Therefore, the amount owed after 7 years, compounded semiannually, on the $2000 loan would be $3895.25, rounded to the nearest cent.

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