SI = (P × R × t)/100
A = P
(1+)t ; CI = A - P
Where,
CI = Compound interest
SI = Simple interest
A = Amount on compound interest
P = Principal
R = rate %
t = time in years
Given, rate is same for calculating both SI and CI
Let the rate be ‘R’.
SI is calculated for 1 year
SI = (P × R × 1)/100 = PR/100
Given, SI = Rs. 260
⇒ PR/100 = 260 -------------eq (1)
CI is calculated for 2 year
∴ A = P
(1+)2 As, CI = A – P
⇒ C. I = P
((1+)2−1) Given, CI = Rs. 540.80
∴ P
((1+)2−1)=540.80-----------eq (2)
Dividing eq 2 by eq 1
= ⇒
=2.08 Using
a2−b2=(a+b)(a−b) ⇒=2.08 ⇒ 2 + R/100 = 2.08
⇒ R = 0.08 × 100 = 8%
Smart Method Total SI for 1st and 2nd year = 260 + 260 = 520
Extra interest for 2nd year = 540.8 - 520 = 20.8
This extra interest is due to interest in 1st year SI.
Hence,
260 × (R/100) = 20.8
⇒ R = (208/10) × (100/260)
⇒ R = 8%