Final answer:
Betty will need to pay $595.51 after three years to settle a loan of $500 with an annually compounded interest rate of 6 percent, as calculated using the future value formula for compound interest. Therefore correct option is A
Step-by-step explanation:
To find out how much Betty will need to pay off the loan at the end of three years with an annually compounded interest rate of 6 percent, we use the formula for compound interest, which is:
Future Value = Principal × (1 + interest rate)time
In this case, the Principal is $500, the interest rate per period (annually) is 0.06 (or 6%), and the time is 3 years. Plugging these into the formula:
Future Value = $500 × (1 + 0.06)3
= $500 × (1.06)3
= $500 × 1.191016
= $595.508, which rounds to $595.51.
Therefore, the correct answer is A) $595.51.