Question

The compound interest, calculated by yearly, on a certain sum of money for the second year is Rs. 864 and the third year is Rs. 933.12. Calculate the rate of interest and the compound interest on the same sum and at the same rate for the fourth year.
(a) 0
(b) Rs.1007.77
(c) Rs.1000
(d) Rs.1100

Answer 1

Hint: First, we will find the rate of interest R by subtracting money of second year from third year which will be simple interest. Then using the formula of simple interest on Rs.864 i.e. $\text{SI=}\dfrac{PRN}{100}$ we have to find the rate of interest. After getting this, we have to directly find compound interest money for fourth year using \[P+RP\] where P is Rs. 933.12.

Complete step-by-step answer:
Here, we have compound interest (CI) for second year as Rs.864 and for third year as Rs.933.12
$\text{CI for }{{\text{2}}^{nd}}\text{ year}=Rs.864$
$\text{CI for }{{\text{3}}^{rd}}\text{ year}=Rs.933.12$
Therefore, simple interest on Rs.864 for one year we will find here which will we get as
$\text{SI=Rs}\text{.933}\text{.12}-\text{Rs}\text{.864}$
$\text{SI=Rs}\text{.69}\text{.12}$
Now, we will use formula of simple interest (SI) given as $\text{SI=}\dfrac{PRN}{100}$
Here we have SI as 69.12, N as 1year, principal amount P as 864 and we have to find rate of interest R
On substituting values, we get
$\Rightarrow \text{69}\text{.12=}\dfrac{864\times R\times 1}{100}$
On making R as subject we get,
$\Rightarrow \dfrac{\text{69}\text{.12}\times \text{100}}{864}\text{=R=}\dfrac{6912}{864}=8\%$
So, we have a rate of interest of 8%.
So, now we will find CI for fourth year by taking principal amount P as 933.12
\[P+8\%P=933.12+\dfrac{8}{100}\left( 933.12 \right)\]
\[=933.12+74.6496\]
\[=1007.77\]
Thus, CI for fourth year is Rs. 1007.77
Hence, option (b) is correct.

Note: Remember that after finding rate of interest, we do not have to find original principal amount P by using compound interest formula as $P{{\left( 1+\dfrac{8}{100} \right)}^{2}}-P\left( 1+\dfrac{8}{100} \right)=864$ and from here on solving P will be Rs. 10000. And then using this principal amount to find the CI for the fourth year will be a very long and time-consuming process and at last the answer will be totally wrong. So, do not make this mistake.