Question

If at the rate of simple interest in percent per annum by which a principal becomes double in 20 years and also amounts to Rs - 720 after 4 years, then find the principal.​

Answer 1

Answer:

Let the Principle = P and Rate of interest = r in decimal

So, in first case, P + P * r * 4 = 720 ……….. (1) and

in second case, P + P * r * 20 = 2P

Or, P * r * 20 = 2P - P = P

Or, 20r = P/P = 1

Or, r = 1/20 = 0.05 i.e, in percentage it is 5%

Now, from equation (1), we get P+ P * 0.05 * 4 = 720

Or, P + 0.2P = 720

Or, P = 720/1.2 = Rs. 600

So, the Principle is Rs. 600 Ans.

Step-by-step explanation:

Check for double the Principle in 20 years = 600 + 600 * 0.05 * 20 = 1200 Proved.

Consider Compound interest :

We have two equations : P * (1+r)^4 = 720 …….. (1) and P * (1+r)^20 = 2P……. (2)

From Eqn (2), P * (1+r)^20 + 2P

Or, (1+r)^20 = 2P/P = 2 Or, 1 + r = 2^(1/20) = 1.035265

Putting the value of 1 + r in Eqn (1), P * ( 1.035265)^4 = 720

Or, P = 720/1.035265^4 = 720/1.1487 = Rs. 626.80 Ans.

Check for double the Principle in 20 years : 626.80 * (1.035265)^20 = 1253.60 Proved.