Question

What sum of money will amount to Rs 13,675.20 in 3 years at compound interest, if the rates of interest are 10%, 11% and 12% for the successive years?

Answer 1

For the third year

Here P = x ; A= Rs 13,675.20 ; t = 1 year; r = 12 % p.a. 

`therefore  "A" = "P" (1 + "r"/100)^"n"`

`=> "Rs"  13675.20 = "x"  (1 + 12/100)^1`

`=> "Rs"  13675.20 = "x" (112/100)`

`=> x = "Rs"  (13675.20 xx 100)/112`

⇒  x = Rs 12, 210 

The sum of money will be Rs 12,210 at the end of the second year or beginnino;; of the third year. 

For the second year 

Here P = x ; A= Rs 12,210 ; t = 1 year ; r = 11 % p.a.

`therefore  "A" = "P" (1 + "r"/100)^"n"`

`=> "Rs"  12210 = "x"  (1 + 11/100)^1`

`=> "Rs"  12210 = "x" (111/100)`

`=> x = "Rs"  (12210 xx 100)/111`

⇒ x = Rs 11, 000 

The sum of money will be Rs 11,000 at the end of the first year or beginning of the second year. 

For the first year 

Here P = x; A= Rs 11,000; t = 1 year; r = 10 % p.a.

`therefore  "A" = "P" (1 + "r"/100)^"n"`

`=> "Rs"  11000 = "x"  (1 + 10/100)^1`

`=> "Rs"  11000 = "x" (11/100)`

`=> x = "Rs"  (11000 xx 10)/11`

⇒ x = Rs 10, 000 

The sum of money will be Rs 10,000 at the beginning of the first year.