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?

Answer 1

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.