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.