Question
On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a.
Hint:
Use the formula of compound interest and simple interest to get the principal amount.
The correct answer is: Rs 10000
Complete step by step solution:
Let the principal amount = P
It is given that the rate of interest R = 5% and number of years T = 2 years.
So, compound interest for 2 years =
Simple interest
for 2 years =
It is given that compound interest - simple interest = 25 Rupees
That is, Rupees.
Hence the principal amount = Rs 10000
Hence the principal amount = Rs 10000
On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?
A. Rs. 24600
B. Rs. 24800
C. Rs. 25200
D. Rs. 25500
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr & {\text{Time = 2 year}} \cr & {\text{Accroding to question,}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right] - \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left( {\frac{{11025 - 10000}}{{10000}}} \right) - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P}}{{10000}} - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P - 1000P}}{{10000}} = 63 \cr & \Rightarrow 25P = Rs.630000 \cr & \Rightarrow P = \frac{{630000}}{{25}} \cr & \Rightarrow P = Rs. 25200 \cr & {\text{Hence}},\,{\text{sum Rs}}{\text{. 25200}} \cr} $$
Click here to read 1000+ Related Questions on Compound Interest(Arithmetic Ability)
On what sum of money does the difference between the simple interest and compound interest in 2 years at 5 % is ₹ 15
Solution
Let the sum of money =x
Simple interest in 2 years =P×R×T100
where P= Principal =x, Rate, R=5% and Time, T=2 years
so Simple Interest =x×5×2100=0.1x
Compound interest:
Amount after 1 year =x+5% of x=1.05x
Amount after 2 years =1.05x+5%(1.05x)=1.05x+0.0525x=1.1025x
So compound interest after 2 years =1.1025x−x=0.1025x
Difference of compound interest and simple interest =0.1025x−0.1x=0.0025x
This difference in interest is given as Rs.15.
So 0.0025x=15
⇒x=150.0025=Rs.6000
Hence, the sum is Rs. 6000