# ARITHMETIC FORMULAE ON COMPOUND INTEREST

1). If P principle is invested with r% pa for n years at compound interest-

*. If Interest is compounded annually then amount is , A = P(1+r/100)^n

*. If Interest is compounded half yearly then amount is , A = P(1+r/200)^2n

*. If interest is compounded quarterly then amount is , A = P(1+r/400)^4n

2). If a city population is P , and it is increasing at the rate of r% annually then-

*. Population after n years –

Population = P(1+r/100)^n

*. Population before n years –

Population = P/(1+r/100)^n

3). If any principle on compound interest become x times in n1 years and y times in n2 years, then = [x^(1/n1) = y^(1/n2)]

4). If the simple interest of any principle for 2 years at the rate of r% annually is SI , then –

Compound Interest = SI(1+r/200)

5). If the simple interest of any principle for 2 years at the rate of r% annually is SI , then the difference between the compound interest and the simple interest is = SI×r/200

6). At compound interest, if any principle become A1 in n years and A2 in (n+1) years then,

*. Rate of compound interest = (A2-A1)100/A1

*. Principle = A1(A1/A2)^n

7). If principle is P and rate is r% pa and time period is 2 years , then –

(CI- SI) = Pr^2/100^2

*. If time period is of 3 years then-

(CI- SI) = Pr^2(300+r)/100^3

8). If time is given in the form of fraction (like 2 1/3 ), then amount A can be given as-

A = P(1+r/100)^2.(1+r/300)

9). If rate of compound interest in first year is r1% , in second year is r2% and in third year it is r3% , then A = P(1+r1/100)(1+r2/100)(1+r3/100)

[Note: This can also apply in calculation of population.]

10). At the rate of compound interest , a principle become Rs x1 in n1 years and become Rs x2 in n2 years , then the rate of interest is –

= {[(x2/x1)^1/(n2-n1)] – 1}%

11). At any principle, the compound interest CI and simple interest SI of two years is given then the principle is = SI^2/4(CI – SI)

12). If the two successive compound interests on any principle for two years is CI1 and CI2 , then the rate of interest is = [(CI2 – CI1)100/CI]%

13). At the rate compound interest , if any principle become x times in n years , then the time taken to become x^y times = y×n

14). If debt of P is used to be pay compounded annually at the rate of r% in n equal installments, then principle is given as –