## Most important topics for CS Foundation Simple Interest

**What is Interest?**

Interest is the consideration paid by the borrower to the moneylender for the use of his money.

The concept of interest involves two persons:

Money Lender (who gives the money)

Borrower (who takes the money)

**Some Related Terms:**

**Principal:**It is the initial value of lending or the sum which is borrowed.**Rate****of Interest:**It is charged for the defined length of time for use of principal. Generally, it is charged on a yearly basis.**Amount:**the final value of an investment. It is the sum total of the principal and interest earned.**Time:**The period for which the money is used.**Interest:**The extra amount charged by the money lender.

** **

__SIMPLE INTEREST__

It is the interest compounded on the principle for the entire period of borrowing.

No interest is paid on interest earned during the term of the loan.

**Formula: **

SI = P*R*T/100

Or SI = A – P

Where,

SI = Simple Interest

P = Principal

R = Rate of Interest

T = Time period

A = Amount

**Example:** How much interest will be earned on Rs. 2000 at 6% simple interest for 2 years?

**Solution :** SI = P*R*T/100

= 2000*6*2/100

= Rs. 240

** Time and Year Fractions**

Interest can be calculated to be paid as half-yearly, quarterly, monthly or daily.

‘T’ needs to be entered as follows:

I = PRT/100 because the interest rate is in units of years.

Half Yearly : T= ½

Quarterly. : T = ¼

Monthly. : T= 1/12

Daily. : T= 1/365

**Example:**** **Find the simple interest for Rs.600 invested at 8.5% for half-yearly.

Solution: I = P x R x T/100

I = 600 ×8.5×1/100×2

I =Rs. 25.50

**Example : **Find the Simple Interest When P = Rs.600, R = 5% per annum, T = Quarterly.

**Solution : **I = P×R×T/100

I= 600×5×1/100×4

I = Rs.7.5

**Example : **Find the Simple Interest when P= 1000, R= 10% per annum, T= 2 months.

**Solution: **I = P×R×T/100

I = 1000×10×2/100×12

I = Rs.16.67

**Example : **Find the Simple Interest when P=500, R=12% per annum, T= 45 days.

**Solution : **I = P×R×T/100

I = 500×12×45/100×365

I = Rs. 7.40

**Formula To Find Final Amount: **

A = P + I

Or A = P(1+ I*T)

Where,

A = Amount

P = Principal

I = Rate /100

T = Time

**Example: **Shweta deposited Rs. 40,000 in a bank for two years with the interest rate of 5.5% p.a. What will be the final value of the investment?

**Solution:** A = P (1 + I*T)

= Rs. 40,000 (1 + 5.5/100*2)

= Rs. 40,000 (1 + 11/100)

= Rs. 40,000*111/100

= Rs. 44,400

**Example : **** **A sum of Rs. 13,500 amounts to Rs. 16,500 in 3years at the rate of simple interest. What is the rate of interest?

**Solution:** Interest = Amount – Principle

Interest = 16500 – 13500

Interest = 3000

R = I×100/P×T

R = 3000×100/12500×3

R = 8%

**Example: **A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed b him was**?**

**Solution: **P = I×100/R×T

P = 5400×100/12×3

P = 15000

**Example: **A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6.5% p.a for 2 years. Find his gain in the transaction per year.

**Solution : **The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest

Simple interest that he needs to pay =

=

= Rs. 400

He also lends it at 6.5% p.a for 2 years

Simple interest that he gets =

=

= 650

His overall gain in 2 years = Rs.650 – Rs.400 = Rs.250

His overall gain in 1 year = 250/2 = Rs.125

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