the difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 3 years is rupees 27.45 find the sum
Answers
Difference Between the Compound and Simple Interest
Sometimes you are given a situation and you have the option of repaying more it through compound interest or through simple interest. Obviously, you will choose simple interest because it is a cheaper option. Also, in compound interest, you are asked to pay the principal amount by levying interest on interest. But you would still need to determine the difference between the compound and simple interest. If the difference asked is for either two or three years than you can easily solve it through the formulas. Here are the formulas to the calculated difference in interests.
Learn more about Simple and Compound Interest in more detail here.
compound and simple interest
If the difference between compound and simple interest is of two years than,
Difference = P(R)²/(100)²
Where P = principal amount, R = rate of interest
If the difference between compound and simple interest is of three years than,
Difference = 3 x P(R)²/(100)² + P (R/100)³.
Here also, P = principal amount, R = rate of interest
Test yourself by answering these 25 Practice Questions set of SI an CI.
Solved Examples
Q. The difference between the compound and simple interest on a certain sum at 12% per annum for two years is Rs. 90. What will be the value of the amount at the end of 3 years if compounded annually?
Ans: Here, in this question, the difference is already given to us and we are required to find the principal amount. And using that principal amount we are required to find the amount compounded after three years. The difference is given for two years. So, the formula will be,
Difference = P(R)²/100²
Now, putting the values into the equation, we will find that,
90 = P(12)²/(100)²
90 x 100²/12² = P
P = Rs. 6250
Now, calculating the compound interest on Rs. 6250 will be,
A = 6250(1 + 12/100)³
A = 6250(112/100)³ => 6250(1.12)³ => Rs. 8780.80
So, the compounded amount after three years will be Rs. 8780.80
Answer:
The answer is ₹ 10,000.
Hope it will help you