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Find the compound interest at the rate of 5 % per annum for 3 years on that principal which in 3 years at the rate of 5 % per annum gives Rs 1200 as simple interest.
Given :
For compound interest:
Rate of interest (R)$=5$%.
Time (N)$=3$ years.
For simple interest:
Rate of interest (R)$=5$%.
Time (N)$=3$ years.
Simple interest (SI)$=1200$.
To do :
We have to find the principal(P) and compound interest(CI).
Solution :
We know that,
$SI = \frac{PNR}{100}$
$1200 = \frac{P \times 3 \times 5}{100}$
$P = \frac{1200 \times 100}{3 \times 5}$
$P = 400 \times 20$
$P = 8000$
The principal is ₹8000.
$CI = P(1+\frac{R}{100})^N - P$
$CI =8000 (1+ \frac{5}{100})^3 - 8000$
$CI = 8000 (\frac{100+5}{100})^3 -8000$
$CI = 8000 (\frac{105}{100})^3 -8000$
$CI = 8000 (\frac{21}{20})^3 - 8000$
$CI = 8000 \times \frac{9261}{8000} - 8000$
$CI = 9261 - 8000 = 1261$
Therefore, the Compound interest is ₹1261.
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