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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.

Answer:

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.

"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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