# SIMPLE INTEREST | fast track arithmetic formulae | shortcut tricks for all competitive examination.

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## ARITHMETIC FORMULAE ON SIMPLE INTEREST

1). Principle = Simple interest ×100/rate×Time
2). Simple interest = principle × rate × time/100
3). Rate = simple interest ×100/principle × time
4). Time = simple interest × 100/ principle × rate
5). Amount = principle + simple interest
6). Principle = amount – simple interest
7). Principle = amount ×100/[100+(rate×time)]
8). If r1% changes to r2% and in t years Rs x receive more , then principle is = 100×x/(r2 – r1)t
9). Time taken by the principle to become n time of itself with r% simple interest is = 100(n-1)/r
10). If any principle become n times of itself in t years then the interest rate = 100(n-1)/t
11). If any principle become n1 times of itself with r1% in any time period , then in same time period, rate required to become n2 times of itself is
= (n2-1)r1/(n1-1)%
12).  If any principle become n1 times of itself in t1 time period in any interest rate, then in same interest rate, time period required to become n2 times of itself is = (n2-1)t1/(n1-1)
13). From the two different banks, Rs x is the difference between in the received interest on the principle P at the time period t , then the difference in their rate of interest is = 100x/Pt
14). If a certain principle is invested at a certain interest rate for t years , then the same principle if invested at r%(more or less) then anyone get Rs x (more or less) , then the principle is = x×100/rt
15). The principle is invested in two parts in such a way that interest received on the first part at r1% interest rate for t1 time period is equal to the interest received on the second part at r2% interest rate for t2 time period , then the ratio of their principle is = 1/r1t1 : 1/r2t2
16). If any principle become Rs x in t1 time period and become Rs y in t2 time period , then the principle is = (xt2 – yt1)/(t2-t1) , and the rate of interest is = (y-x)100/(xt2 – yt1)
17). The annual payment that will discharge a debt of Rs P due in T yrs at the interest rate of r% is
= 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.