Question

The compound interest on a sum for 2 years at 12% per annum is
Rupees 510. What would the simple interest on the same sum at the same rate for the same period

Answer 1

Given,

For Compound Interest ( CI ),
Rate of interest, R = 12 % p.a.
Time, T = 2 years
Compound Interest, CI = ₹ 510

We know that,

CI = P { ( 1 + R / 100 ) ^ T - 1 }
510 = P { ( 1 + 12 / 100 ) ^ 2 - 1 }
510 = P { ( 112 / 100 * 112 / 100 ) - 1 }
510 = P { 12,544 / 10,000 - 1 }
510 = P { 2,544 / 10,000 }
P = 510 * 2,544 / 10,000
P = 51 * 2,544 / 1,000
P = 1,29,744 / 1,000

Now for SI,
P = ₹ 1,29,744 / 1,000
R = 12 % p.a.
T = 2 years

Simple Interest, SI = ( P * R * T ) / 100
SI = $\frac{( \frac{129744}{1000} \times 12 \times 2)}{100}$

SI = $\frac{129744 \times 12 \times 2}{1000 \times 100}$

SI = 31,13,856 / 1,00,000

SI = ₹ 31.13856

On rounding off,

SI = ₹ 31.14