# If simple interest of a certain sum of money for 1 year is ₹50 and compound interest for 2 years is ₹102, let us write by calculating the sum of money and the rate of interest.

Let the principal = ₹p and the rate of interest per annum = r%

The interest for 1 year at the rate of simple interest r% per annum

Again the amount at the rate of compound interest r% per annum for 2 years

Compound interest for 2 years

By the condition, … (1)

… (2)

Dividing equation (2) by (1),

1/2 r = 102 – 100

1/2 r = 2

r = 2 × 2

r = 4

From (1),

p = 50 × 25

p = 1250

Principal is ₹1250 and rate of interest is 4%.

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