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Question
What sum of money will amount to Rs 3,326.40 in 3 years at compound interest, if the rates of interest are 8%, 10% and 12% for the successive years?
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Solution
For the third year
Here P = x ; A= Rs 3,326.40 ; t = 1 year ; r = 12 % p.a.
`therefore "A" = "P" (1 + "r"/100)^"n"`
`=> "Rs" 3326.40 = "x" (1 + 12/100)^1`
`=> "Rs" 3326.40 = "x" (112/100) `
`=> "x" = "Rs" (3326.40 xx 100)/112`
`=> "x" "Rs" 2970`
The sum of money will be Rs 2, 970 at the end of the second year or beginning of the third year.
For the second year
Here P = x ; A= Rs 2,970 ; t = 1 year ; r = 10 % p.a .
`therefore "A" = "P" (1 + "r"/100)^"n"`
`=> "Rs" 2970 = "x" (1 + 10/100)^1`
`=> "Rs" 2970 = "x" (11/10) `
`=> "x" = "Rs" (2970 xx 10)/11`
⇒ x = Rs 2700
The sum of money will be Rs 2, 700 at the end of the first year or beginning of the second year.
For the first year
Here P = x ; A= Rs 2,700 ; t = 1 year ; r = 8 % p.a .
`therefore "A" = "P" (1 + "r"/100)^"n"`
`=> "Rs" 2700 = "x" (1 + 8/100)^1`
`=> "Rs" 2700 = "x" (108/100) `
`=> "x" = "Rs" (2700 xx 100)/108`
⇒ x = Rs 2500
The sum of money will be Rs 2,500 at the beginning of the first year.
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