If the simple interest on a sum of money at 5% p.a. for 3 years is Rs. 1200, the compound interest on the same sum for the same period at the same rate is
Solution
Correct Answer: Option B
Let, the sum is P.
We know that, formula for simple interest:
\(S.I.\; = \frac{{P \times R \times T}}{{100}}\)
Where,
S.I. = Simple Interest
P= principal
T = Time
R = Rate of interest
∴ SI = P × (5/100) × 3 = 1200
⇒ P = 8000
We know the formula for compound interest-
\(\Rightarrow {\mathbf{CI}} = \left[ {{\mathbf{P}}\left\{ {{{\left( {1 + \frac{{\mathbf{R}}}{{100}}} \right)}^T} - 1} \right\}} \right]\)
Where,
CI = Compound interest
P = Principal
R = Rate of interest
T = Time period
\(CI\; = \;8000\;\left[ {{{\left( {1\; + \frac{5}{{100}}} \right)}^3}\;-\;1\left] {\; = \;8000} \right[{{\left( {\frac{{21}}{{20}}} \right)}^3}-1} \right]\;\)
∴ CI= 1261
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