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.

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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

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