Question

At what rate percent compound interest per annum will the compound interest
on Rs 1.25.000 be Rs 91.000 in 3 years?
Ans:20%​

Answer 1

Answer:

• The rate of interest will bee 20% to make the condition true

Step-by-step explanation:

Given :-

• Compound Interest = 91,000
• Principal Amount = 1,25,000
• Time Period = 3 years

To Find :-

• The rate of interest

Formula to be used :-

${\purple{\bigstar{\underline{\boxed{\frak{ A = P \bigg[ 1 + \dfrac{r}{100} \bigg]^n}}}}}}$

Where :-

• A stands for Amount
• P stands for Principal
• R stands for Rate of Interest
• N stands for No of years

We know that :-

• Amount = Principal + Interest
• Amount = 1,25,00 + 91,000
• Amount = Rs. 216000

Here,

• Amount = 216000
• Time = 3 years
• Principal = 125000

Required Solution :

$:\implies \bf A = P \bigg[ 1 + \dfrac{r}{100} \bigg]^n$

$:\implies \bf 216000 = 125000 \bigg[ 1 + \dfrac{r}{100} \bigg]^3$

$:\implies \bf \dfrac{216\cancel{000}}{125\cancel{000}} = \bigg[ 1 + \dfrac{r}{100} \bigg]^3$

$:\implies \bf \dfrac{216}{125} = \bigg[ 1 + \dfrac{r}{100} \bigg]^3$

$:\implies \bf \bigg(\dfrac{6}{5}\bigg) ^{\cancel3} = \bigg[ 1 + \dfrac{r}{100} \bigg]^{\cancel3}$

$:\implies \bf \dfrac{6}{5} = 1 + \dfrac{r}{100}$

$:\implies \bf \dfrac{6}{5} - 1 = \dfrac{r}{100}$

$:\implies \bf \dfrac{6}{5} - \dfrac{5}{5} = \dfrac{r}{100}$

$:\implies \bf \dfrac{1}{5} = \dfrac{r}{100}$

$:\implies \bf r = \dfrac{1}{5} \times 100$

$:\implies \bf r = 20 \%$

Therefore :

• The rate of interest will bee 20% to make the condition true

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