Question

A sum at a given rate of interest becomes 1200 in 4 yrs. 2000 in 5 yrs. what was that sum.​

Answer 1

Given :- A sum at a given rate of interest becomes 1200 in 4 yrs. 2000 in 5 yrs. what was that sum. ?

Answer :-

Let us assume that, the sum was given at simple interest .

so,

→ Amount in 4 years = 1200

→ Amount in 5 years = 2000

then,

→ Interest recived in 1 year = 2000 - 1200 = 800 .

since in this interest will be same in each year .

then

→ Interest in 4 years will be = 800 * 4 = 2400 which is greater than amount ..

So , this case in not possible.

Now let interest is at compound interest .

then, Let principal is Rs.P and rate is R% compounded annually .

so,

→ P[1 + (R/100)]⁴ = 1200

→ P[1 + (R/100)]⁵ = 2000

dividing both ,

→ P[1 + (R/100)]⁵ / P[1 + (R/100)]⁴ = 2000/1200

→ [1 + (R/100)] = 5/3

→ (R/100) = 5/3 - 1

→ R/100 = (2/3)

→ R = (200/3) % (Ans.)

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Answer 2

Given :  A sum at a given rate of interest becomes 1200 in 4 yrs. 2000 in 5 yrs.  

To Find : the sum.​

Solution:

Let say sum = P

Rate of interest = R

A = P ( 1 + R/100)ⁿ

n = number of years

A = amount after n years

in 4 years  = P ( 1 + R/100)⁴  = 1200

in 5 years  = P ( 1 + R/100)⁵  = 2000

=>  ( 1 + R/100)⁵ /  ( 1 + R/100)⁴   = 2000/1200

=> ( 1 + R/100) = 5/3

P ( 1 + R/100)⁴  = 1200

=> P ( 5/3)⁴  = 1200

=> P  =   1200 * 3⁴ / 5⁴

=> P = 155.52

Sum = 155.52

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