Simple interest accrued on a certain sum is 16/25 of the principal sum. If the…
2022
Simple interest accrued on a certain sum is 16/25 of the principal sum. If the numerical value of the annual interest rate (%) and the time (years) are equal, what is the annual rate of interest?
Answer: D. 8% — CONCEPTFor simple interest, the interest on principal P at annual rate r% for t years is I = Prt/100. Dividing by P gives I/P = rt/100. If r and t have the…
- A.
10%
- B.
7%
- C.
6%
- D.
8%
Attempted by 5 students.
Show answer & explanation
Correct answer: D
CONCEPT
For simple interest, the interest on principal P at annual rate r% for t years is I = Prt/100.
Dividing by P gives I/P = rt/100. If r and t have the same numerical value x, then I/P = x2/100.
APPLICATION
Let the common numerical value of the annual rate and the time be x; thus r = t = x.
The given ratio is I/P = 16/25.
Substitute r = t = x into I/P = rt/100 to obtain x2/100 = 16/25.
Multiplying by 100 gives x2 = 64.
Since a rate and a time are positive here, x = 8.
CROSS-CHECK
Substituting r = 8 and t = 8 gives I/P = (8 × 8)/100 = 64/100 = 16/25, which reproduces the given ratio.
Therefore, the annual rate of interest is 8%.