# 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

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by aparna0

5750 in how many years ? Clarify

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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. 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

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

Let us say

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