Question : Simple interest on a certain sum is one-fourth of the sum and the interest rate per annum is four times the number of years. If the rate of interest increases by 2%, then how much will the simple interest (in INR) be on INR 3,600 for 6 years?
Option 1: 2,562
Option 2: 2,514
Option 3: 2,642
Option 4: 2,592
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Correct Answer: 2,592
Solution :
Let P be the principal sum.
Simple Interest, SI = $\frac{1}{4}$×P
Number of years = n
Interest rate, R = 4n
SI = $\frac{P×R×T}{100}$
$\frac{P}{4}$ = $\frac{P×n×4n}{100}$
⇒ $n^2 = \frac{100}{4×4}$
⇒ $n = \frac{10}{4} = 2.5$
R = 4 × 2.5 = 10%
Now, R + 2 = 12%
P = INR 3600
n = 6
SI = $\frac{P×R×T}{100}$
= $\frac{3600×12×6}{100}$
= 2592
Hence, the correct answer is 2592.
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