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

Question 21 Compound Interest Exercise 2.2

A certain sum amounts to ₹ 5292 in 2 years and to ₹ 5556.60 in 3 years at compound interest. Find the

rate and the sum.

It is given that

Amount after 2 years = ₹ 5292

Amount after 3 years = ₹ 5556.60

So the difference = 5556.60 – 5292 = ₹ 264.60

Here ₹ 264.60 is the interest on ₹ 5292 for one year

We know that

Rate % = (SI × 100)/ (P × t)

Substituting the values

= (264.60 × 100)/ (5292 × 1)

Multiply and divide by 100

= (26460 × 100)/ (100 × 5292)

= 5%

Here

\begin{aligned} &\mathrm{A}=\mathrm{P}(1+\mathrm{r} / 100)^{\mathrm{n}}\\ &\text { Substituting the values }\\ &5292=\mathrm{P}(1+5 / 100)^{2} \end{aligned}

By further calculation

\begin{aligned} &\mathrm{P}=5292 \div(1+5 / 100)^{2}\\ &\text { So we get }\\ &\mathrm{P}=5292 \div(21 / 20)^{2} \end{aligned}

P = 5292 × 21/20 × 21/20

P = ₹ 4800

Hence, the rate is 5% and the sum is ₹ 4800.

Video transcript
"hey guys welcome to leto q a video i am vinit your lido tutor bringing you this question on your screen so a certain sum amounts to rupees five to nine two in two years and two rupees five five five six point six in three years at compound interest find the rate and the sum okay let's do this what is given to us amount is given to us as rupees five to nine two time is given to us as two years right and amount 2 is given to us as rupees 5556.60 and time 2 is equal to 3 years right so what we can say is the interest element in the third year is the amount in the third year minus amount in the first year because it is uh compound interest so amount at the second end of second year is the principal at the end of first year right great or the principle at the beginning of third year therefore interest for third year is equal to rupees five five five six point six minus five to nine two this is equal to rupees so 5556.6 minus 5292 is 264.6 this is the interest right now we know interest for one year is equal to prt by 100 this implies 264.6 is equal to 5 to 92 into r into 1 by 100 this implies rate of interest is equal to 264 into 100 is 60 by 5 to 90. right guys so 26460 divided by 5292 will be equal to 5 therefore rate of interest is 5 now we have to find the sum right now the amount at the end of second year is 5292 so 5292 by principal amount is equal to principal into 5 by 100 to the power 2 because 2 years this implies 5292 is equal to p into 105 by 100 can be written as 21 by 20 into 21 by 20. this implies p is equal to 5292 into 20 into 20 by 21 into 21 is 441 so 5292 divided by 441 is 12 this is equal to 12 into 2 into 2 into 100 so this is equal to rupees 4800 is the principle isn't that easy guys right so 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 practicing"
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