A sum of Rs. 2000 yields Rs. 180 with simple interest in nine 9 months. The annual rate of interest is
12%
To find the annual rate of interest, we must use the formula for simple interest:
\(SI = \frac{P \cdot R \cdot T}{100}\)
where:
- SI is the simple interest
- P is the principal amount
- R is the rate of interest per annum
- T is the time period in years
Given:
- \(SI = 180\) (as it yields Rs. 180 as interest)
- \(P = 2000\) (the principal amount is Rs. 2000)
- \(T = \frac{9}{12}\) years (since 9 months is \(\frac{3}{4}\) of a year)
Substituting the given values into the simple interest formula:
\(180 = \frac{2000 \cdot R \cdot \frac{3}{4}}{100}\)
Solving for \(R\) (the rate of interest):
First, simplify the equation:
\(180 = \frac{2000 \cdot R \cdot 0.75}{100}\)
\(180 = 20 \cdot R \cdot 0.75\)
\(180 = 15R\)
Solve for \(R\):
\(R = \frac{180}{15}\)
\(R = 12\)
Thus, the annual rate of interest is 12%.
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A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
