If the simple interest on a sum of money for 2 years at \(5 \%\) per anum is \(\approx 50\), what is the compound interest on the same sum at same rate for the same time?
A. N51.25 B. N\(50.25\) C. N49.25 D. N\(\N48.25\)
Correct Answer: A
Explanation
let \(P=\) the sum \(=\) principal given: \(I=N 50\) $$ \begin{array}{l} \mathrm{R}=5 \% \\ \mathrm{~T}=2 \text { years } \\ \mathrm{I}=\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100} \\ \mathrm{P}=\frac{1 \times 100}{\mathrm{R} \times \mathrm{T}} \\ \mathrm{P}=\frac{50 \times 100}{5 \times 2}=\mathrm{N} 500 \\ \text { for compound interest } \\ \text { Amount }=\mathrm{C} . \mathrm{I} \text { + Principal } \\ \text { C. I. }=\mathrm{A}-\mathrm{P} \\ \Rightarrow \mathrm{C}-\mathrm{I}=\mathrm{P}(1+\mathrm{R} \%)^{\mathrm{n}}-500 \\ \quad=500\left(1+\frac{5}{100}\right)^{2}-500 \\ =500(1+0.05)^{2}-500 \\ =500(1.05)^{2}-500=\frac{\mathrm{N}}{2} 51.25 \end{array} $$
