CI and SI - Difference Formulas

When the rate of interest is 12%, SI = 5000*3*12/100

In the case of compound interest, Amount = $$P(1+r)^n$$

CI = Amount - P = $$P(1+r)^n - P$$

CI = $$5000(1+12/100)^3 - 5000$$

CI - SI = $$5000(1+12/100)^3 - 5000 - 5000*3*12/100 = 224.64$$

Alternate Method:

Amount = $$P(1+r)^n$$

CI = Amount - P = $$P(1+r)^n - P$$

CI = $$5000(1+r/100)^3 - 5000$$

SI = 5000*3*r/100

CI - SI = $$5000(1+r/100)^3 - 5000 - 5000*3*r/100 =  224.64$$

Let R= r/100

CI - SI = $$5000(1+R)^3 - 5000 - 5000*3*R = 224.64$$

= $$(1+R)^3 - 1 - 3*R = 224.64/5000$$

=$$R^3+ 1+3R^2+3R - 1 - 3*R = 224.64/5000$$

=$$R^3+3R^2  = 224.64/5000$$

Solving the cubic equation we will get R=0.12

r= 12%

Let principal be P. SI for 2 years = P*2*10/100 = P/5. CI for 2 years = P(1+10/100)^2 - P = 21P/100. Therefore, difference in interest amount = P/100 = 1000 => P = 1,00,000. SI for 3 years = 30000. CI for 3 years = 33100. Difference = 3100.