An amount of $255 is invested at 8.5% per annum simple interest. To the nearest year, how long will it take to earn $86.70 in interest under simple interest?

Introduction:
This question tests solving for time in simple interest when the interest amount is given. The formula SI = (P * r * t)/100 can be rearranged to t = (SI * 100)/(P * r). Since the rate is per annum and the answer is requested in years, we can compute t directly in years. Finally, because the question asks “to the nearest year,” we confirm whether the computed value is essentially 4 years or needs rounding up/down.

Given Data / Assumptions:

• Principal P = $255
• Rate r = 8.5% per annum
• Simple interest SI = $86.70
• Time t = ? years
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Rearrange to solve for time: t = (SI * 100) / (P * r). Substitute the values. Keep r as 8.5 (percent form) because the formula divides by 100. Compute the quotient accurately and then round to the nearest whole year as requested.

Step-by-Step Solution:
t = (SI * 100) / (P * r) t = (86.70 * 100) / (255 * 8.5) Numerator = 8670 Denominator = 255 * 8.5 = 2167.5 t = 8670 / 2167.5 = 4.0 Nearest year = 4 years

Verification / Alternative check:
Interest per year at 8.5% on $255 is (255*8.5)/100 = 21.675. Over 4 years, SI = 21.675 * 4 = 86.70 exactly, confirming t = 4 years without any rounding ambiguity.

Why Other Options Are Wrong:
2 years gives only $43.35, 3 years gives $65.025, and 5 years gives $108.375. Only 4 years yields exactly $86.70.

Common Pitfalls:
Using 0.085 while still dividing by 100, mixing up interest with final amount, or rounding too early in intermediate multiplication/division steps.

Final Answer:
It will take 4 years.