Final answer:
Riley and Clayton made errors when calculating compound interest on Riley's loan. The correct future value of the loan after 6 years is $12,017.42. Clayton's estimate was close, suggesting a minor miscalculation, while Riley's was significantly off, pointing to a fundamental misunderstanding or calculation error.
Step-by-step explanation:
To determine the correct amount that Riley will owe at the end of 6 years, we need to use the compound interest formula: A = P(1 + r/n)^(nt). Here, A stands for the future value of the loan, P is the principal amount ($8000), r is the annual interest rate (7.1% or 0.071), n is the number of times interest is compounded per year (semi-annually, so 2), and t is the time the money is invested or borrowed for (6 years).
Calculating the future value, we get: A = 8000(1 + 0.071/2)^(2*6) = 8000(1 + 0.0355)^(12) = 8000(1.0355)^(12) = 8000 * 1.502177 = $12,017.42.
This correct amount is very close to what Clayton thought Riley would owe ($12,073.32). Clayton's slight miscalculation might have come from using an incorrect number of compounding periods or a rounding error in the calculations. It seems Riley had the larger error in his estimate of $11,406, which likely resulted from a misunderstanding of how compound interest works or a basic calculation mistake.