Final answer:
Rachel would owe $33,417.98 after 10 years without making payments on an $8000 loan at 15% interest compounded quarterly. The amount Rachel will owe is not listed in the given options, suggesting a possible error in the provided choices.
Step-by-step explanation:
Rachel borrowed $8000 at a rate of 15%, compounded quarterly. To calculate the amount owed after 10 years with no payments made, we use the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times the interest is compounded per year, and t is the time in years.
Let's plug in Rachel's loan details: P = $8000, r = 0.15, n = 4 (quarterly), and t = 10. So we have:
A = $8000(1 + 0.15/4)^(4*10)
A = $8000(1 + 0.0375)^(40)
A = $8000(1.0375)^(40)
A = $8000(4.17724693)
A = $33,417.97544
After rounding to the nearest cent, Rachel will owe $33,417.98 after 10 years without making any payments.
This means the correct answer is not listed in the options given. Therefore, we must acknowledge a possible error in the presented choices.