A sum of money becomes Rs 4000 after three years and Rs 8000 after six years on compound interest The sum is .....?

Answer 1

Rs 2000.

The amount a after n years of an amount c with interest rate r % is:

a = c(1 + r/100)^n

After 3 & 6 years of the question there is:

Rs 4000 = c(1 + r/100)^3

Rs 8000 = c(1 + r/100)^6

Dividing the second by the first gives:

Rs 8000 ÷ Rs 4000 = (c(1 + r/100)^6) ÷ (c(1 + r/100)^3)

→ 2 = (1 + r/100)^3

Using the first equation and substituting for (1 + r/100)^3 found above:

Rs 4000 = c(1 + r/100)^3 = 2c

→ c = Rs 2000

Alternatively:

As it is compound interest, the saved interest also attracts interest; the amount doubles in the 3 years from year 3 to year 6, so it doubles every 3 years.

Therefore initially it must be half the value at 3 years

→ it is ½ × Rs 4000 = Rs 2000.