# Simple Interest

The interest calculated only on the original principal throughout the time period is called Simple Interest, that is, original principal alone produces interest. No interest is calculated on the interest generated after each time period.S.I. depends on 3 factors: the principal, rate of interest and the term of loan (time period). Simple interest is directly proportional to the principal (S.I. ∝ *P*). It is also directly proportional to the time period (S.I. ∝ *T *) and the rate of interest (S.I. ∝ *R*).

Putting together the above three relations, the simple interest on a given principal *P* for a time period *T* and at a rate of interest *R*% is calculated using the relation,

The amount *A* to be returned at the end of the time period is the sum of the principal *P* and the simple interest,

*A* = *P* + S.I.

Sometimes, we have to calculate the rate of interest, when we know the amount accumulated on a principal after two different time periods. In such cases, we can find the rate of interest using the relation

If two different principals are lent out at two different rates of interest, then the rate of interest on the overall principal is calculated using the relation,

*P*= ₹50

*R*= 2%

*T*= 6 months

*P*= ₹120

*R*= 2% p.a. S.I. = ₹20

*P*= ₹5,600 S.I. = ₹500

*T*= 2 years

*R*= 2% p.a.

*T*= 5 years

*A*= 40,000

*T*= 10 years

The time given is irrelevant here. We can simply find the principal as

Amount = Principal + S.I. ⇒ Principal = Amount – S.I.

⇒ Principal = 40,000 – 10,000

⇒ Principal = ₹30,000

*P*

_{1}= ₹150

*P*

_{2}= ₹100

*R*

_{1}= 15% p.a.

*R*

_{2}= 10% p.a.

We can directly apply the formula for calculating rate in case of two different principals at two different rates.