Question

At what Rate percent per annum will ₹50,000 amount to ₹86,400 in 3 years,if the Interest is Compounded Annually?

All The Best! :D​

Answer 1

Answer:

20 rate percent

Step-by-step explanation:

principle =50000

amount=86400

time=3years

Formula=A=p(1+r/100)^n

86400=50000(1+r/100)^3

86400÷50000=(1+r/100)^3

216/125=(1+r/100)^3

(6/5)^3=(1+r/100)^3

6/5=(1+r/100)

(6/5)-1=r/100

1/5=r/100

By cross multiplication

r5=100

r=100/5

r=20

Answer 2

Given : ₹50,000 amount to ₹86,400 in 3 years, if the Interest is Compounded Annually.

To Find : Rate of Percent ?

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Solution : Principal (P) = Rs. 50000

$~~~~~~~~~~~~~~~~~$Amount (A) = Rs. 86400

$~~~~~~~~~~~~~~~~~$Time (T) = 3 years

$~$

$\underline{\frak{As ~we ~know~ that~:}}$

• $\boxed{\sf\pink{A~=~P \bigg(1~+~\dfrac{R}{100}\bigg)^n}}$†

$~$

Where,

• "P" is Principal
• "A" is Amount
• "R" is rate of interest
• "n" is time.

$~$

$\pmb{\sf{According~ to~ the ~Given ~Question~:}}$

$~$

${\sf\qquad\qquad:\implies{A~=~P \bigg(1~+~\dfrac{R}{100}\bigg)^2}}$

${\sf\qquad\qquad:\implies{86400~=~50000\bigg(1~+~\dfrac{R}{100}\bigg)^3}}$

${\sf\qquad\qquad:\implies{\dfrac{86400}{50000}~=~\bigg(1~+~\dfrac{R}{100}\bigg)^3}}$

${\sf\qquad\qquad:\implies{\dfrac{864}{500}~=~\bigg(1~+~\dfrac{R}{100}\bigg)^3}}$

${\sf\qquad\qquad:\implies{\dfrac{216}{125}~=~\bigg(1~+~\dfrac{R}{100}\bigg)^3}}$

${\sf\qquad\qquad:\implies{\dfrac{^{3}√216}{125}~=~1~+~\dfrac{R}{100}}}$

${\sf\qquad\qquad:\implies{\dfrac{6}{5}~=~1~+~\dfrac{R}{100}}}$

${\sf\qquad\qquad:\implies{\dfrac{6}{5}~-~1~=~\dfrac{R}{100}}}$

${\sf\qquad\qquad:\implies{\dfrac{6~-~5}{5}~-~1~=~\dfrac{R}{100}}}$

${\sf\qquad\qquad:\implies{\dfrac{1}{5}~=~\dfrac{R}{100}}}$

${\sf\qquad\qquad:\implies{100~=~5R}}$

${\sf\qquad\qquad:\implies{R~=~\dfrac{100}{5}}}$

${\sf\qquad\qquad:\implies{R~=~\cancel\dfrac{100}{5}}}$

$\qquad\qquad:\implies{\boxed{\underline{\frak{\purple{R~=~20\%}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{The~Rate~of~interest~is~\bf{\underline{20\%}}}}$

$~$

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$\pmb{\frak{More ~Information~:}}$

• A is used for Amount.
• P is used for Principal.
• R is used for Rate of interest.
• N is used for Time.

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