Question

a sum of money lent at compound interest amount to 1815 in two years and to 1996.50 in 3 years find the sum and rate percent​

Answer 1

Answer:-

• Sum = ₹1500

• Rate of interest = 10% p.a.

Explanation :-

Let the sum be Rs.P and the rate be R%.

We know that :-

=> A = P(1 + R/100)ᵗ

When t = 2 yrs :-

=> 1815 = P(1 + R/100)². ----(1)

When t = 3 yrs :-

=> 1996.50 = P(1 + R/100)³ ----(2)

On dividing eq.2 by eq.1, we get :-

=>1996.50/1815=[P(1+R/100)²]/[P(1+R/100)³]

=> 1.1 = 1 + R/100

=> 1.1 = 100 + R/100

=> 110 = 100 + R

=> R = 110-100

=> R = 10%

Now, let's put the value of P in eq.1 to find the required sum :-

=> 1815 = P(1 + 10/100)²

=> 1815 = P( 110/100 × 110/100)

=> 1815 = 121P/100

=> P = 1815×100/121

=> P = 181500/121

=> P = ₹1500

Thus :-

• Sum is ₹1500

• Rate of interest is 10% p.a.

Answer 2

Between 2 and 3 years the money has increased to 1996.5/1815 = 1.1 which is an increase of 0.1 or 10%.

If P is the original sum then

1815 = P(1.1)² and P = 1815/1.21 = ₹1500.