Question

a sum of money becomes 4 times in 3 years, find the rate of compound interest​

Answer 1

Given : A sum of money becomes 4 times in 3 years,

To find  :  the rate of compound interest​

Solution:

Principal = P

Rate of interest = R % per annum

Time = n = 3 years

A = 4P

A = P (1 + R/100)ⁿ

=> 4P  =P (1  + R/100)³

=>  4 = (1 + R/100)³

=> 1 + R/100 =  1.5874

=> R/100  = 0.5874

=> R = 58.74  %

Hence rate of compound interest​  = 58.74  %  per annum

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Answer 2

Given:

The sum of money becomes 4 times in 3 years.

i.e. time t = 3 years

To find:

rate of compound interest​ R =?

Step-by-step explanation:

• The compound interest is the difference between the amount invested in an investment and the actual future value of the investment.

• Mathematically, compound interest is expressed as

A= P$(1+R)^t$               ...(1)

where

A = compound interest

P = principle value

R = rate of compound interest​

t = Number of years of deposit

• In problem, given that, a sum of money will become 4 times in 3 years.

• Suppose P be the amount that is invested.

• Hence, after 3 years, the final amount becomes 4 times of original.

       i.e. A = 4P & t = 3

• Put these values in equation(1)

        4P = P ( 1+ $R)^3$

• After solving the above equation we get,

       R = 0.8374 %

Hence the rate of compound interest​ is 0.8374 % per year.