if simple interest on a certain sum of money is 2.56 times the principle and…
2026
if simple interest on a certain sum of money is 2.56 times the principle and the rate of interest per annum equals the number of years then the rate of interest is?
- A.
12%
- B.
14%
- C.
16%
- D.
23%
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Show answer & explanation
Correct answer: C
Key idea: let the annual rate be r% and the time be r years (rate equals number of years).
Simple interest = (principal × rate × time) / 100 = P × r × r / 100 = P × (r^2 / 100).
Given simple interest is 2.56 times the principal, so r^2 / 100 = 2.56.
Solve: r^2 = 2.56 × 100 = 256, so r = √256 = 16. (Take the positive root for a positive interest rate.)
Therefore the rate of interest is 16%.
Quick check: (16 × 16) / 100 = 256/100 = 2.56 times the principal, which matches the given information.