Question

In How Many Years Will A Sum Of Money Double At 5 P.A. Compound Interest

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Time=20\:years}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt:\implies Amount = 2 \times principal \\ \\ \tt: \implies Rate\% = 5\% \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Time(t) = ?$

• According to given question :

$\circ\: \text{Let \: principal \: be \: x} \\ \\ \circ \:\text{Amount = 2x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a = p(1 + \frac{tr}{100} ) \\ \\ \tt: \implies 2x = x(1 + \frac{5t}{100} )\\ \\ \tt: \implies \frac{2x}{x} = (1 + 0.05t) \\ \\ \tt: \implies 2-1 =0.05t$

$\tt: \implies 1 = 0.05t \\ \\ \tt: \implies t = \frac{1}{0.05} \\ \\ \green{\tt: \implies t = 20 \: years}$

Answer 2

$\bf \red { \underline{Given}}$

• Principal = P
• Amount = 2P
• Rate = 5°/•

$\bf \red { \underline{To \: find \: out }}$

Time = ?

$\bf \red { \underline{Solution}}$

We know that,

Simple interest (S.I)= Amount - Principal

= 2P - P

= P

Now,

$Time, t = \frac{SI \times 100}{P \times R}$

$\implies\: \frac{ \cancel{ \: P} \times 100}{ \cancel {\: P} \times 5}$

$\implies \: 20$

Knowledge Enhancer

• Principal(P): The money taken by the borrower from the lender is called Principal.

• Amount (A): The total money given by the borrower to the lender is called Amount.

• Time (T): The time after which the money is to be returned is called Time.