What is the future value of $124.49 after earning simple interest for five years at an annual rate of 10%?

Question

BlackTom AI · Accepted Answer

Simple interest formula A = P(1 + rt) applies because interest is earned at a fixed annual rate without compounding.

Relevant knowledge:
- P = principal = $124.49
- r = annual interest rate = 10% = 0.10
- t = time in years = 5
- Simple interest amount = P · r · t
- Future value A = P + (P · r · t) = P(1 + r t)

Step-by-step calculation:
1. Compute yearly interest: P · r = 124.49 × 0.10 = 12.449 (dollars per year).
2. Compute total interest for 5 years: 12.449 × 5 = 62.245.
3. Add interest to principal to get future value: 124.49 + 62.245 = 186.735.
4. Round to the nearest cent: 186.735 → $186.74.

Why this is correct:
- The simple interest formula was used correctly; interest accrues linearly (no compounding), so total interest is P × r × t.
- The computed future value $186.735 rounded to two decimal places yields $186.74, which matches the correct answer.

Why the other options are incorrect:
- $200.49 equals 124.49 × (1.1)^5, the future value under annual compound interest, not simple interest, so it is not correct here.
- $136.94 equals approximately one year of simple interest (124.49 + 12.449 ≈ 136.939 → $136.94), not five years.
- $162.25 and $175.00 do not match the total after 5 years of simple interest (they correspond to other incorrect time/rate combinations or rounding errors) and so are incorrect.

Conclusion: The future value after 5 years of simple interest at 10% is $186.74, which matches the provided correct answer.

What is the future value of $124.49 after earning simple interest for five years at an annual rate of 10%? 单项选择题

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