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I = (P * R * T ) / 100 Where R is the rate of interest, P is the principal amount, T is the time period of interest in years and I is the interest.

Principal amount ( P ) = $ 500

Time period (T) = 1 year

Interest ( I ) = $ 50

For finding the rate of simple interest we use the interest rate equation, I = (P * R * T ) / 100

Now put the values in the equation,

50 = (500 * R * 1) / 100

50 = 500R/ 100

50 * 100 = (500R / 100) * 100

5000 = 500R

5000/500 = 500R / 500

R = 10

Thus the rate of interest is 10 %.

I = (P * R * T ) / 100

We are given I = $ 20, P = $ 200, T = 2 years.

20 = ( 200 * R * 2 ) / 100

20 = 400 R / 100

20 = 4R

20 /4 = 4R/R

R = 5

Thus the annual rate of interest is 5%.