Question

The difference between the compound interest and the simple interest on Rs.42000 for two years is Rs.105 at the same rate of interest per annum. Find the
(i)the rate of interest
(ii)the compound interest earned in second year

Answer 1

Hint: We have the difference of simple interest and compound interest. We have to first find the simple interest and compound interest with help of difference of both of them. For solving this question, you should know the formula of simple and compound interest.

Complete step-by-step answer:
We have the difference
S.I - C.I = 105
And the principle value = 42000
We know the formula of simple interest
$ = \dfrac{{P.R.T}}{{100}}$
Here P = principle value, R = rate of interest and T= time
Putting the values in the formula
$ = \dfrac{{42000.r.2}}{{100}}$
$ = 840r$
Now we have to find the compound interest
A = $P{(1 + \dfrac{r}{{100}})^t}$
Here A = final amount
Putting the values
$ = 42000{(1 + \dfrac{r}{{100}})^2}$
= $42000(1 + \dfrac{{{r^{}}}}{{10000}} + \dfrac{r}{{50}})$
$ = 42000 + \dfrac{{42{r^2}}}{{10}} + 840r$
Now we know that
C.I = A – P
C.I = $42000 + \dfrac{{42{r^2}}}{{10}} + 840r$$ - 42000$
C.I = $ = \dfrac{{42{r^2}}}{{10}} + 840r$
We have given in the question that the difference between the S.I and C.I is 105
S.I – C.I = 105
$840r + $$\dfrac{{42{r^2}}}{{10}} - 840r = 105$
$\dfrac{{42{r^2}}}{{10}} = 105$
$42{r^2} = 105.10$
${r^2} = \dfrac{{105.10}}{{42}}$
${r^2} = 25$
$r = \sqrt {25} $
$r = 5$
Interest rate is $5%$
So, we have a rate of interest of 5%.
Now we have to find the compound interest at second year
 We can find the compound interest
C.I = A – P
C.I = $42000{(1 + \dfrac{5}{{100}})^2} - 42000$
C.I = $42000(1 + \dfrac{{25}}{{10000}} + \dfrac{1}{{10}}) - 42000$
C.I = $4305$

Compound interest at second year is $4305$.

Note: Simple interest is based on the principal amount of a loan. Compound interest is based on the principal amount and the interest which is being added for every period of time.