# Word Problem 10

**Problem 10: On a certain investment simple interest is applied at certain rate. The amount doubles in 20 years term. After how many years the amount will be quadrupled ?**

**Solution: **

Here are situations of two cases, First case is given as 20 years period, and second case duration is to be found in which interest amount will be four times !

Case 1

In 20 years period

We know

Where,

P = Principal amount ( Amount in the beginning or investment amount)

I = Interest on principal amount

A= total amount at the end, which is sum of initial amount and interest incurred.

According to condition, amount ‘A’ doubles in 20 years i-e

Put in relation (1), this value of ‘A’, we get

It means interest will be equal to principal amount in 20 years !

*Case-2*

In second case we want amount ‘A’ to become four times i-e

Put this value in eq (1) above, we get;

Now equation (2) says ‘I’ the interest will be equal to ‘P’ in 20 years i-e P is equal to interest of 20 years or we can say ‘P’ is the amount of 20 years. So we can take

P=20 years

So we put P = 20 years in eq(3)

or

**It means after interest of 60 years the amount will be 4 times !**

**Or we can say in 20 years the amount will be quadrupled**

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