# Finding Rate of Interest

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For finding rate of interest P. a , we use the formula of amount only.

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