Question

6. Kiran invested 1000 in a finance company and received 1331 after 3 years. Find the rate of interest
percent per annum compounded annually.​

Answer 1

Answer:

r=10 rate of interest per annum is 10

Answer 2

Given:-

• Principal (P) = Rs.1000
• Amount (A) = Rs.1331
• Time (t) = 3 years

To Find:-

The rate of interest per annum compounded annually.

Solution:-

We know,

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

Now,

Putting the values,

$\sf{1331 = 1000\bigg(1+\dfrac{r}{100}\bigg)^3}$

= $\sf{\dfrac{1331}{1000} = \bigg(\dfrac{100+r}{100}\bigg)^3}$

= $\sf{\bigg(\dfrac{11}{10}\bigg)^3 = \bigg(\dfrac{100+r}{100}\bigg)^3}$

As the powers are same,

$\sf{\dfrac{11}{10} = \dfrac{100+r}{100}}$

By Cross-multiplication,

= $\sf{11\times 100 = 10(100+r)}$

= $\sf{1100 = 1000 + 10r}$

= $\sf{1100-1000 = 10r}$

= $\sf{100 = 10r}$

= $\sf{r = \dfrac{100}{10}}$

= $\sf{r = 10\%}$

Therefore, Rate of interest is 10%.

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How did I get the answer?

✓ We know, to find CI we first need yo find the amount.

For finding amount we have the formula:-

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

Here we put all the values from the given. After putting the values we come at a point where the powers on both LHS and RHS is same. Here we apply the law of indices which states that $\sf{If\:a^n = b^n\:then\:a=b}$. After that on equating we get the value of r.

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Explore More!!!

To find CI after finding Amount we apply the formulas as:-

CI = Amount - Principal.

More formulas:-

When the Principal is compounded half yearly, the formula to find amount is as follows:-

$\sf{A = P\bigg(1+\dfrac{r}{200}\bigg)^2t}$

When the principal is compounded quarterly the formula for finding amount is as follows:-

$\sf{A = P\bigg(1+\dfrac{r}{400}\bigg)^4t}$

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