# A certain sum of money amounts to Rs 6500 in 3 years and Rs 5750 in respectively. Find the principal and the rate percent

1
by aparna0
5750 in how many years ? Clarify

2014-12-22T04:30:06+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Is it simple interest or  compound interest ?

For the amount  Rs 5, 750 -  in how many years ?

Let us say n years.

1. Simple interest case

Rs 6, 500 =  P ( 1 + r * 3 )
Rs 5, 750 =  P ( 1 + r * n )

750 = P * r * (3 - n)
6,500/5,750 = (1+3r) / (1+n r)
6500 + 6500 n r = 5750 + 3 * 5750 * r
750 = r ( 1725 - 650 * n )

r = 30 / ( 69 - 26 n )    = rate of interest
P = 750 /  [ (3-n) r ]  = 25 (69 - 26 n) / (3-n)

2. Compound interest,
the number of years after which  the amount is Rs 5, 750 =  n years

6,500 = P ( 1 + r )^3
5750 = P ( 1 + r)^n

6500 / 5750 = (1+r)^(3-n)
=>        r  = - 1 +  [ 1/(3-n) ] * Log (650/575)
=>        P = 6,500 / (1 +r )^3