# 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

2014-12-22T04:27:10+05:30

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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. If it is compound interest, then it is more difficult, with out knowing the number of years after which  the amount is Rs 5, 750.

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