# Finding Rate of Interest

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**A = ( 1 + r)**

^{n}Where, A = amount

P = Principal

r = rate in percent

n = time in years.

**Examples on finding rate of interest:**

1) At what rate percent P.a , compound interest will $ 10,000 amount to $ 13,310 in three years?

**Solution :**

Here, P = $ 10,000 ; A = $ 13,310 ; n = 3 years

A = P ( 1 + r)

^{n}

13,310 = 10,000( 1 + r )

^{3}

13,310/10,000 = ( 1 + r )

^{3}

1331/1000 = ( 1 + r)

^{3}

( 11/10)

^{3}= ( 1 + r)

^{3}

**As the exponents are same the bases are equal.**

11/10 = 1 + r

11/10 – 1 = r

( 11 – 10)/10 = r

1/10 = r

As rate is in percent so, r = (1/10) x 100

Rate = 10 % P.a.

2) At what rate percent compound interest P.a. will $640 amount to $ 774.40 in 2 years ?

**Solution :**

Here, P = $ 640 ; A = $ 774.40 ; n = 2 years

A = P ( 1 + r)

^{n}

774.40 = 640 ( 1 + r )

^{2}

774.40 /640 = ( 1 + r )

^{2}

77440 /64000 = ( 1 + r)

^{2}

( 88/80)

^{2}= ( 1 + r)

^{2}

(11/10)

^{2}= ( 1 + r)

^{2}

**As the exponents are same the bases are equal.**

11/10 = 1 + r

11/10 – 1 = r

( 11 – 10)/10 = r

1/10 = r

As rate is in percent so, r = (1/10) x 100

Rate = 10 % P.a.

**Compound Interest ( CI )**

• Find Compound Interest when interest is compounded Half yearly

• Find Compound Interest when interest is compounded Quarterly

• Find CI when interest is compounded annually but Rates are different

• Finding Principal

• Finding Time Period of Investment

• Finding Rate of Interest

• Find Compound Interest when interest is compounded Half yearly

• Find Compound Interest when interest is compounded Quarterly

• Find CI when interest is compounded annually but Rates are different

• Finding Principal

• Finding Time Period of Investment

• Finding Rate of Interest

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