The amount owed at the end of 2 years on a $5,600 loan with 7% interest compounded monthly can be calculated with the compound interest formula, which results in a future value that does not match the provided options, indicating a potential mistake.
The question is about calculating the future value of a loan with compound interest. To find the amount owed at the end of 2 years on a $5,600 loan with a 7% interest rate compounded monthly, we use the compound interest formula: Future Value = Principal x (1 + (Interest Rate / Number of Times Compounded))^ (Number of Times Compounded x Time).
Let's plug in the values: Future Value = $5,600 x (1 + (0.07 / 12))^(12 x 2). Simplifying inside the parentheses first:
(1 + (0.07 / 12)) = 1 + 0.00583333 = 1.00583333.
Now raising this to the 24th power (12 months x 2 years) gives us approximately 1.1498588. Multiplying this result by the principal value of $5,600 gives us the future value, which is equal to approximately $6,439.21. However, none of the given options matches this calculated value, so it's possible there may have been a mistake in the calculation, information provided, or options listed.
the correct future value should match one of the given options A through D. However, based on the standard compound interest formula, the calculated amount doesn't match any of the presented options, which indicates a need to recheck the numbers and information provided.