The compound interest on a sum of money in 2 years and 4 years are Rs 5,460 and Rs 12,066.60
respectively. Find the difference between principal
and compound interest of 3 years.

The difference between the principal and the compound interest in three years is Rs 17,994

Step-by-step explanation:

The compound interest is given according to the following formula;

The given amount of the compound after 2 years = Rs 5,460

The given amount of the compound after 4 years = Rs 12,066.60

Therefore, we have;

...(1)

...(2)

Dividing equation (2) by (1), we have;

∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)

∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)

12,066.60/5,460 = x + 1

x =  12,066.60/5,460 - 1 = 1.21 = 121/100

x = 121/100

We get

r = 100 × 0.1 = 10%

r = 10%

Therefore, we have;

The principal = Rs. 26,000

The compound interest in 3 years is therefore;

The difference, 'd', between the principal and the compound interest in three years, is given as follows;

d = P - CI₃

d = 26,600 - 8606 = 17994

The difference between the principal and the compound interest in three years, d = Rs 17,994.

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step-by-step explanation: