**Rule of 72 for Compound Interest :**

**Rule of 72 for Compound Interest :**

t = 72/R (The value is a close approximation)

t is the time taken for an amount to Double

R is the Rate of Interest

Example: In how many years will an amount X double at 20% p.a.??

t = 72/20 = 3.6 years

**Difference Between Compound Interest(CI) & Simple Interest (SI):**

**Difference Between Compound Interest(CI) & Simple Interest (SI):**

**When T = 2 years:**

**When T = 2 years:**

CI-SI=P×(R/100)^2

CI-SI=(R×SI)/(2×100)

Example: If the difference between CI and SI is Rs.10, for a period of 2 years and for a principal of Rs.1000 then find the rate of interest?

10=1000 x (R/100)^2

Therefore R = 100 %

**When T = 3 years:**

**When T = 3 years:**

CI -SI=[(PR)^2/(10)^4] * ((300+R)/100 )

CI-SI= SI/3 * [(R/100)^2 + (3R/100)]

Example: If the difference between CI and SI is 100 for a period of 3 years at a rate of interest of 100 percent p.a. then find the Simple Interest(SI)?

100=SI/3 * [(100/100)^2 + (3×100/100)] Therefore SI = 300/4 = Rs.75

**When Money Becomes “N” times:**

**When Money Becomes “N” times:**

**For SI:**

**For SI:**

RT=(n-1)×100

Example: In how many years will an amount become 6 times of it, at a rate of interest of 10% p.a.?

10 x T = (6-1) x 100 ; T = 500/10 = 50 years

**For CI:**

**For CI:**

R=100×[(n)^(1/t) -1]

Example: An amount becomes 8 times of it in 3 years Compounded annually. Find the Rate of Interest?

R = 100 X [8^(1/3) -1] = 100 [2 – 1] = 100 %