On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to rupees 25?

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ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.2 in Chapter 2 - Compound Interest

Question 28 Compound Interest Exercise 2.2

. On what sum of money will the difference between the compound interest and interest for 2 years be

equal to ₹ 25 if the rate of interest charged for both is 5% p.a.

Answer:

It is given that

Sum (P) = ₹ 100

Rate (R) = 5% p.a.

Period (n) = 2 years

We know that

SI = PRT/100

Substituting the values

= (100 × 5 × 2)/ 100

= ₹ 10

So the amount when interest is compounded annually = P (1 + R/100)

n

Substituting the values

\begin{aligned} &=100(1+5 / 100)^{2}\\ &\text { By further calculatio }\\ &=100 \times(21 / 20)^{2} \end{aligned}

So we get

= ₹ 441/4

Here

CI = A – P

Substituting the values

= 441/4 – 100

= ₹ 41/4

So the difference between CI and SI = 41/4 – 10 = ₹ ¼

If the difference is ₹ ¼ then sum = ₹ 100

If the difference is ₹ 25 then sum = (100 × 4)/ 1 × 25 = ₹ 10000

Video transcript

"hey kids welcome to lido q a video i am vinit your leader tutor bringing you this question on your screen on what sum of money friends between the compound interest and the interest for two years be equal to rupees 25 if the rate of interest charge for both is five percent per annum now the difference between the compound interest and interest for two years be equal to 25 so this means the difference between the interest for the first year and the second year is 25 percent so let us take an example to understand this let us say we you invest 10 000 rupees on the first year again the interest component is ten thousand rupees sorry thousand rupees and the principal is again ten thousand in the second year again you get thousand rupees on this 10 000 and 100 rupees on this interest right so these are the two components of compound interest interest on principle and interest on interest now this difference of 100 rupees between the interest of two consecutive year is the interest on the interest of the first year so we are going to use the same concept here right now interest on interest of first year is equal to rupees 25 right now interest on interest of first year is rupees 25 so interest of first year becomes our principle therefore interest of first year will be the principle now simple interest is equal to p rt by 100 this implies 25 is equal to p into 5 by 100 into 1 so this is 1 by 20. so this implies p is equal to 500 so this is the interest on first year now interest of first year is equal to rupees 500 therefore we can say 500 is equal to the actual sum of money into rate by 100 into 1. so this implies p is equal to 500 into 100 by 5 so this will be equal to rupees 10 000 isn't it isn't it easy guys right if you still have a doubt please leave a comment below do like the video and subscribe to our channel i'll see you in our next video until then bye guys keep learning keep flourishing and keep"

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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 = PIt 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 RupeesThat is,  Rupees.Hence the principal amount = Rs 10000

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