Henry bought an antique watch for $6,000 and sold it 9-months later for $6,360. What simple interest rate did he earn on this sale?

Question

BlackTom AI · Accepted Answer

To analyze this problem, I’ll break down the given facts and then test each choice against the simple interest formula.
First, determine the interest earned: selling price minus purchase price = 6,360 − 6,000 = 360 dollars. This is the interest obtained over the holding period of 9 months, which is 0.75 years.
Now apply the simple interest formula: Interest = Principal × Rate × Time, or I = P × r × t. We know I = 360, P = 6,000, and t = 0.75.
Solving for r gives r = I / (P × t) = 360 / (6,000 × 0.75) = 360 / 4,500 = 0.08, which is 8%.
Option-by-option review:
- 8.08%: This is slightly higher than the calculated 8%. Since r = 360 / 4,500 equals exactly 0.08, 8.08% would imply earned interest of 4,500 × 0.0808 ≈ 363.6, which does not match the actual 360; thus this is incorrect.
- 6.00%: If r were 6%, the interest would be 6,000 × 0.06 × 0.75 = 270, which is less than the actual 360; therefore this option is inconsistent with the data.
- 7.55%: This would yield interest of 6,000 × 0.0755 × 0.75 ≈ 340. 5, still short of 360, so this choice is not correct.
- 8.00%: With r = 0.08, the interest computes to 6,000 × 0.08 × 0.75 = 360, exactly matching the observed interest; this aligns perfectly with the given numbers.
In summary, while several options are close, only 8.00% reproduces the exact interest earned over the 9-month holding period using simple interest, confirming it as the correct rate.

Henry bought an antique watch for $6,000 and sold it 9-months later for $6,360. What simple interest rate did he earn on this sale?Single choice

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