Question from Simple Interest - Mathematics ?

Question

If the compound interest on a certain sum for 2 years is Rs.21.What could be the simple interest.???...Answer---Rs.20..HOW.???..

Answer 1

Compound interest at rate R for 2 years accumulates to: (1+R)^2=1.21 implies R=10%.

At R=10%, simple interest in 2 years accumulates to 2*(1+10%)=1.20, implies interest only is .20

Answer 2

For compound interest
F = P(1 + i)^n
For simple interest,
F = P(1 + ni)
For either,
I = F - P
for compound,
I = P[(1 + i)^n - 1]
P = I/[1 + i)^n - 1]
for simple,
I = inP
P = I/ni
so
21/[(1 + i)^2 - 1] = 20/2i
42i = 20(1 + 2i + i^2 - 1)
42i = 40i + 20i^2
10i = 21 - 20
i = 1/10 = 10%
P = Rs1.00 or Rs.100 (not sure if the period goes with the abbreviation or the number)

Answer 3

If Compound Interest is given then calculate the principal amount
p=Compound Interest / [{(1+R/100)^n}-1]

and then use this P for calculating the Simple Interest.