# Finding Rate when Principal and Time are given

In this section you will learn finding rate when principal and time are given in easy way.

The formula is given below :

S.I x 100
Rate % = R = -------------
P x T

Amount = A = P + S.I

Example :

1) P = \$ 20,000 Amount = \$ 21,800 and time T = 2 years. Find the rate.

Solution :
Amount = P + S.I

21,800 = 20,000 + S.I

S.I = 21,800 - 20,000

S.I = \$ 1,800

S.I x 100
Rate % = R = -------------
P x T

1800 x 100
Rate % = R = -------------
20,000 x 2

180,000
Rate % = R = -------------
40,000

Rate = 4.5%

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2) P = \$ 625 Amount = \$ 641.25 and time T = 146 days. Find the rate.

Solution :
Amount = P + S.I

641.25 = 625 + S.I

S.I =641.25 - 625

S.I = \$ 16.25

S.I x 100
Rate % = R = -------------
P x T

As the rate is given in days so T = 146 days = 146/365 =0.4 years

16.25 x 100
Rate % = R = -------------
625 x 0.4

1625
Rate % = R = -------------
250

Rate = 6.5%
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3) At what rate percent will a sum of money treble itself in 12 years?

Solution :
A = 3P
t = 12 years
A = P + I
But I = PRT/100
∴ A = P - (PRT/100)
3P = P - (PRx12/100)
3P- P = 12PRT/100
2P = (12 x P x R)/100
cross multiply
2P x 100 = 12 PR
200P = 12 PR
R = 200P/12P
∴ R = 200/12
∴ R = 50/3 % = 16.66%

Simple Interest (S.I)

Finding rate when Principal and time are given
Finding time when Principal and rate are given
Solved examples on Simple Interest