John has been promised $720 of interest after 9 months of investing $8,000 with Commonwealth Bank. What rate of simple interest is John earning per annum?
约翰在联邦银行投资8000美元9个月后，被承诺获得720美元的利息。约翰每年的简单利率是多少？

Question

BlackTom AI · Accepted Answer

Simple interest uses I = P × r × t, so r = I / (P × t).

Relevant points: I is the interest earned, P is the principal, r is the annual simple interest rate (expressed as a decimal), and t is the time in years. Months must be converted to years: 9 months = 9/12 = 3/4 = 0.75 years.

Step-by-step calculation:
1. Convert time to years: t = 9/12 = 0.75.
2. Compute the denominator P × t: 8000 × 0.75 = 6000.
3. Solve for r: r = I / (P × t) = 720 / 6000.
4. Compute the fraction: 720 ÷ 6000 = 0.12.
5. Convert to percent: 0.12 × 100% = 12.00%.

Why this is correct: plugging r = 12.00% back into the simple interest formula gives I = 8000 × 0.12 × 0.75 = 8000 × 0.09 = 720, which matches the promised interest. Therefore the annual simple interest rate is 12.00%.

Why the other options are incorrect (briefly):
- 12.18% would produce I = 8000 × 0.1218 × 0.75 = 730.80, which is more than the promised $720.
- 11.01% would produce I = 8000 × 0.1101 × 0.75 = 660.60, which is less than $720.
- 9.00% would produce I = 8000 × 0.09 × 0.75 = 540.00, also less than $720.

Conclusion: The correct annual simple interest rate is 12.00%, matching the provided answer.

John has been promised $720 of interest after 9 months of investing $8,000 with Commonwealth Bank. What rate of simple interest is John earning per annum? 约翰在联邦银行投资8000美元9个月后，被承诺获得720美元的利息。约翰每年的简单利率是多少？单项选择题

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