Question

The amounts on a certain principal for 3 years and 4 years at a certain rate of c.I are rs.18,250.50 and rs.20,988.10. What is the rate of interest?

Answer 1

total interest=20988.10-18250.50
=2737.6
20988.10*x=2737.6
x=15%
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Answer 2

Let consider the rate of interest = R%

The amounts on a certain principal for 3 years at a certain rate of c.I=Rs.18,250.5

A =  P ( 1 + R/100)ⁿ

Rs.18,250.5 = P (1 + R /100)³     -----------------------   (1)

The amounts on a certain principal for 4 years at a certain rate of c.I=Rs20,988.10.

A=P (1 + r/100 )ⁿ

Rs20,988.10. = P ( 1 + R/100)⁴  -----------------------(2)

Let's divide (2) ÷(1)

(Rs 20988.10)÷( 18250.50) =[ P ( 1 + R/100)⁴ ] ÷[ P ( 1 + R/ 100 )³]

                                            =  ( 1 + R /100)

(Rs 20988.10)÷( 18250.50)-1   = R/100

[ (20988.10) -( 18250.50)]÷( 18250.50) = R/100

(2737.6 ) ÷( 18250.50)= R/100

∴R = $\frac{273760}{18250.50}$ = 15.000137

Hence rate of interest ( R) will be 15%

Ans - Rate of interest will be 15%.

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