Math, asked by Prabhat0027, 7 months ago

If the CI on a sum for 2 years at 4% p.a. is ₹408, the the SI on the same sum at the same rate and for the same rate and for the same period is?

Answers

Answered by Cosmique

Given :

C.I. on a sum = Rs. 408
Time period for C.I. , t = 2 years
Rate of interest per annum, R = 4 %

To find :

S.I. on the same sum at the same rate and for the same period of time = ?

Knowledge required :

Formula to calculate S.I.

$\red{\bigstar}\boxed{\sf{S.I.=\dfrac{P\times R\times t }{100}}}$

Formula to calculate C.I.

$\red{\bigstar}\boxed{\sf{C.I.=P\left(1+\dfrac{R}{100}\right)^t-P}}$

[ Where P is the principal sum, R is the rate of interest per annum, t is time period ]

Solution :

Let, principal money = P

then,

Using formula for calculating C.I. to find the value of P

$\longrightarrow\sf{C.I.=P\left(1+\dfrac{R}{100}\right)^t-P}$

$\longrightarrow\sf{408=P\left(1+\dfrac{4}{100}\right)^2-P}$

$\longrightarrow\sf{408=P\left(1+\dfrac{16}{10000}+\dfrac{8}{100}\right)-P}$

$\longrightarrow\sf{408=P\left(1+\dfrac{16}{10000}+\dfrac{8}{100}-1\right)}$

$\longrightarrow\sf{408=P\left(\dfrac{16+800}{10000}\right)}$

$\longrightarrow\sf{4080000=816\;P}$

$\longrightarrow\underline{\underline{\red{\sf{P=5000\;\;Rs}}}}$

Now,

Using formula to calculate S.I. to find the S.I. on the same sum , interest rate and period of time

$\longrightarrow\sf{S.I.=\dfrac{P\times R\times t }{100}}$

$\longrightarrow\sf{S.I.=\dfrac{5000\times 4\times 2}{100}}$

$\longrightarrow\sf{S.I.=50\times 4\times 2}$

$\longrightarrow\underline{\underline{\large{\red{\sf{S.I.=400\;\;Rs}}}}}$

therefore,

Simple Interest on the same principal sum, time period and interest rate will be 400 Rs.

Answered by Rudranil420