Question

The ratio of the amount for two years under compound interest annually and for one year under simple interest is 6:5. When the rate of interest is the same, then find the value of rate of interest?

Answer 1

Hint: To get the value of rate of interest of this problem we will find out the total payable amount on the basis of compound interest and the total payable amount on the basis of simple interest for one year. Then we take the ratio of both of them and equate it with the given ratio in the question such that we can get the value of the rate of interest.

Complete step-by-step answer:
Let the principle = P, Rate = r % per annum
So the total payable amount on compound interest mode after two year.
Will be,
 \[P\left( {1 + \dfrac{r}{{100}}} \right){^2}\]
The total amount payable after one year on simple interest mode
We get,
$p\left( {1 + \dfrac{{r \times 1}}{{100}}} \right)$
Now the ratio is given as $\dfrac{6}{5}$
​Now taking the ratio of both the mode according to the question
We get
$\dfrac{{P\left( {1 + \dfrac{r}{{100}}} \right){^2}}}{{p\left( {1 + \dfrac{{r \times 1}}{{100}}} \right)}} = \dfrac{6}{5}$
on simplifying we get,
 \[\left( {1 + \dfrac{r}{{100}}} \right) = \dfrac{6}{5}\]
Or,
 \[ \Rightarrow \dfrac{r}{{100}} = \dfrac{6}{5} - 1 = \dfrac{1}{5}\]
Or,
 \[r = \dfrac{{100}}{5} = 20\]
∴ rate of interest \[ = 20\% \]
So, the correct answer is “\[ = 20\% \] ”.

Note: If any amount compounded annually then at the end of the first year the payable amount will be the same for both the simple interest mode and compound interest mode. But from next year onward always the compound interest mode is greater than the simple interest mode.