Question

Sum of money becomes 1.44 times in 2 years Find the rate of Interest if Amount Compounded annually

Answer 1

50. If a sum of money compounded annually becomes 1.44 times of itself in 2 years, then the rate of interest per annum is. 25%

Answer 2

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{The\ sum\ of\ money\ becomes\ 1.44\ times\ in\ 2\ years.} \\ &\sf{The\ amount\ is\ compounded\ annually. } \end{cases}$

To find:- We have to find the rate of interest if Amount is compounded annually ?

☯️ Let P is the principal of sum of money and R is the rate of interest.

Since:-

$\sf : \implies {Amount\ =\ 1.44\ \times\ P.}$

$\sf : \implies {Time\ =\ 2\ years.}$

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {A\ =\ P\ \bigg (1\ +\ \dfrac{R}{100} \bigg)^T.}$

Here:-

• A, is for amount.
• P, is for principal.
• R, is for rate.
• T, is for time.

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$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {A\ =\ P\ \bigg (1\ +\ \dfrac{R}{100} \bigg)^T} \\ \\ \sf : \implies {1.44P\ =\ P\ \bigg (1\ +\ \dfrac{R}{100} \bigg)^2} \\ \\ \sf : \implies {\bigg (1\ +\ \dfrac{R}{100} \bigg)^2\ =\ 1.44} \\ \\ \sf : \implies {1\ +\ \dfrac{R}{100}\ =\ 1.2} \\ \\ \sf : \implies {\dfrac{R}{100}\ =\ 0.2} \\ \\ \sf : \implies {R\ =\ 0.2\ \times\ 100} \\ \\ \sf : \implies {\purple{\underline{\fbox{\bf R\ =\ 20\ \%.}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ required\ rate\ of\ interest\ is\ 20\ \%.}}$