Delhi Police Constable Exam Model Paper 5

GIVEN:
A sum of Rs. P becomes Rs. 3P in 5 years when invested at compound interest.
CONCEPT:
Compound interest concept.
FORMULA USED:
Amount $=\mathit{P}\times {\left(1+\frac{\mathit{R}}{100}\right)}^{\mathit{T}}$
Where,
P = Principal, R = Rate, T = Time
CALCULATION:
Principal = Rs. P,
⇒ Amount after 5 years = 3P
According to the question,
$3\mathit{P}=\mathit{P}\times {\left(1+\frac{\mathit{R}}{100}\right)}^5$
⇒ ${\left(1+\frac{\mathit{R}}{100}\right)}^5=3----\left(\mathit{i}\right)$
Now,
Time = 15
⇒ $\mathit{A}=\mathit{P}\times {\left(1+\frac{\mathit{R}}{100}\right)}^{15}$
⇒ $\mathit{A}=\mathit{P}\times {\left[\left(1+\frac{\mathit{R}}{100}\right)5\right]}^3$
From equation (i):
A = $\mathit{P}\times 3^3$
⇒ A = 27P
∴ The sum will be 27P times after 15 years.
Short Trick
In case of Compound interest:
If a sum becomes ‘x’ times in ‘t’ years:
It will be $‘{\mathit{x}}^2’$ times in ‘2t’ years.
It will be ‘ ${\mathit{x}}^3$ ’ times in ‘3t’ years and so on.
Hence,
A sum becomes 3 times in 5 years when invested at compound interest, it will be $27\left(=3^3\right)$ times in $15\left(=3\times 5\right)$ years