Question

the ratio of 3 year compound interest and simple interest for 1 year is 3 : 64 : 1 on a certain sum of money at a rate of r​

Answer 1

Answer:

The ratio of 3 years of CI and SI of one year on a certain sum confiscated of money is 3.64:1. What is the rate of percentage?

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Ved Prakash Sharma

Answered 6 months ago

Let the sum of money is ₹ P. and rate of interest is r% p.a. .

Compound interest for 3 years = P.[(1+r/100)^3 -1].

= P.[1+3.1.(r/100).(1+r/100)+(r/100)^3 -1].

= P.(r/100).(3+3.r/100+ r^2/10000)……………….(1).

Simple interest for one year = P.r.1/100. …………………..(2). , accordingly :-

P.(r/100).(3+3.r/100 +r^2/10000)/P.(r/100) = 3.64/1.

or, 3+3.r/100+r^2/10000 = 3.64

or, r^2/10000 + 3.r/100 - 0.64 = 0

or, r^2 + 300.r -6400 = 0.

or, r^2+320.r -20.r -6400 =0.

or, r.(r+320) -20.(r+320) =0

or, (r+320).(r-20) =0.

r = - 320% (not valid) , or 20 % , Answer.

Explanation:

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