Question

The difference between the compound interest and simple interest on a certain sum for 2 years at 6% per annum is Rs 90. Find the sum

Answer 1

let the sum be P = Rs. 100.

time T = 2 years, rate of interest R = 6% per annum

simple interest =  PRT/100= 100*6*2/100=
Rs 12

compound amount= P( 1+R/ 100)^T
= 100*(1+6/100) ^2
= 112.36

therefore the compound interest = compound amount - principal

=112.36-100=12.36/-

the difference between the compound interest and simple interest = 12.36-12.00 = 0.36/-

if the difference between the CI and SI is Rs. 0.36 the principal = Rs. 100

if the difference between the CI and SI is Rs. 90 the principal = 100/0.36*90
= 25000

thus the sum is Rs. 25000.

hope this helps you.

Answer 2

Answer:

P=25000

Step-by-step explanation:

Let sum = P

Interest rate = 6% per annum

Time = 2 years

Simple interest (SI) = PRT/100 [Where, P = Present value

R = Annual interest rate

T = Time in years]

∴ SI = (P × 6 × 2)/100

⇒ SI = 3P/25 __________ (i)

Compound interest (CI) = P (1 + R/100)n - P [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ CI = P (1 + 6/100)2 - P

⇒ CI = P (1 + 3/50)2 - P

⇒ CI = P (53/50)2 - P

⇒ CI = (2809P/2500)- P

⇒ CI = (2809P – 2500P)/2500

⇒ CI = 309P/2500 ______ (ii)

Now,

CI – SI = (309P/2500) – (3P/25)

⇒ 90 = (309P/2500) – (3P/25) [Given, CI – SI = 90]

⇒ 90 = (309P – 300P)/2500

⇒ 90 = 9P/2500

⇒ P = 90 × 2500/9

⇒ P = 10 × 2500

⇒ P = 25000

∴ Sum = Rs.25000

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