## ARITHMETIC FORMULAE ON SIMPLE INTEREST

= 100P/[100T + rT(T – 1)/2]18). If A1 is the amount of principle P at time period t with r1% interest rate , and A2 is the amount of principle if rate of simple interest is r2% , then principle P is = (A2r1 – A1r2)/(r1 – r2) and time period t is = (A2 – A1)100/(A2r1 – A1r2)

19). A1 is the amount of principle P in time period t1 with any interest rate r% , and A2 is the amount of principle if time period is t2 , then principle P is = (A2t1 – A1t2)/(t1 – t2) and interest rate is

= (A2 – A1)100/(A2t1 – A1t2)

20). SI1 is the simple interest of a principle P1 in t1 years with r1% interest rate. And SI2 is the simple interest of a principle P2 in t2 years with r2% interest rate , then difference in simple interest is

SI2 – SI1 = (P2r2t2 – P1r1t1)/100

If only time changes and all parameters are constant then-

*. SI2 – SI1 = Pr(t2 – t1)/100

*. If only rates changes then-

SI2 – SI1 = Pt(r2 – r1)/100

*. If only principle changes then –

SI2 – SI1 = rt(P2 – P1)/100

IF TWO PARAMETERS CHANGES

*. Only change in rate and time then-

SI2 – SI1 = P(r2t2 – r1t1)/100

*. Only change in principle and time

SI2 – SI1 = r(P2t2 – P1t1)/100

*. Only change in principle and rate

SI2 – SI1 = t(P2r2 – P1r1)/100

21). If 1/x part of a principle P is lent out at r1% rate, 1/y part is at r2% rate and remaining 1/z part is at r3% interest rate , and in this way simple interest received is SI , then

Principle P is = SI × 100/(r1/x +r2/y + r3/z)

22). The rate on which simple interest become n times of principle in t years is = 100n/t

23). Simple interest if amount is given –

SI = A × r × t/(100 + rt)

24). If a principle P is given to the bank in n equal installments at r% rate per annum , then amount of each installment is = P(1+ nr/100)

#### 25) Mind it

*. If rate of interest is half yearly then rate and time is = r/2% and 2t

*. If rate of interest is quarterly then rate and time is = r/4% and 4t

*. If rate of interest is monthly then rate and time is = r/12% and 12t.