# 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

• Finding rate when Principal and time are given

• Finding time when Principal and rate are given

• Solved examples on Simple Interest