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Chau borrowed $8000 at a rate of 13.5%, compounded semiannually. Assuming he makes no payments, how much will he owe after 10 years? Do not round any intermediate computations, and round your answer to the nearest cent. ?

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Final answer:

Chau will owe approximately $28,968.76 on an $8000 loan at a rate of 13.5%, compounded semiannually after 10 years with no payments made.

Step-by-step explanation:

The question asks us to calculate the future value of an investment with interest compounded semiannually. Chau borrowed $8000 at an interest rate of 13.5%, compounded semiannually. To find out how much he will owe after 10 years without making any payments, we use the compound interest formula:

A = P(1 + rac{r}{n})^{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 unit t.

t is the time the money is invested for, in years.

For Chau's loan:

P = $8000

r = 13.5% or 0.135 (as a decimal)

n = 2 (since it is compounded semiannually)

t = 10 years

Now we substitute the values into the formula:

A = 8000(1 + rac{0.135}{2})^{2 imes 10}

A = 8000(1 + 0.0675)^{20}

A = 8000(1.0675)^{20}

A = 8000(3.62109474865)

A ≈ $28,968.76

After 10 years, with no payments made, Chau will owe approximately $28,968.76.

It is essential to not round intermediate computations to ensure the accuracy of the final answer.

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