When we borrow money we are expected to pay for using it – this is called interest.

There are three components to calculate simple interest: **principal** (the amount of money borrowed),** interest rate** and **time**.

**Formula for calculating simple interest:**

I = Prt

Where,

I = interest

P = principal

r = interest rate (per year)

t = time (in years or fraction of a year)

**CALCULATING SIMPLE INTEREST EXAMPLES**

Example:

Alan borrowed $10,000 from the bank to purchase a car. He agreed to repay the amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).

If he repays the full amount of $ 10,000 in eight months, the interest would be:

P = $ 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)

Applying the above formula, interest would be

I = $ 10,000(0.10)(8/12)

= $ 667

If he repays the amount of $10,000 in fifteen months, the only change is with time. Therefore, his interest would be:

I = $ 10,000 (0.10)(15/12)

= $ 1,250

**The Bankers Rule:**

In the world of finance, time is often expressed in days rather than months. Two kinds of times are used: Exact time and Approximate time.

**Exact Time**

It uses the precise number of days for time of the loan or investment. Assumes that each year has 360 days.

Approximate time: Assumes that each year has 360 days and each month has 30 days.

**The Bankers rule**

Is widely used in the United States, and uses the combination of ordinary interest and exact time.

Example: An investment of $5,000 is made on August 31 and repaid on December 31 at an interest rate of 9%

Applying the Bankers rule, interest would be:

I = Prt

= $5,000(0.09)(106/360)

= $ 132.50

**Determining the maturity value:**

Maturity value = Interest + Principal

Formula: S = P (1 + rt)

Refer the example given under the Bankers rule. Maturity value would be,

S = $ 5,000 [1 + 0.09(106/360)]

= $ 5,000 (1.0265)

= $ 5,132.50

Note: How to calculate 1.0265. First, divide 106 by 360, you will get 0.2944. Then, multiply 0.2944 by 0.09, you will get 0.0265. Add 1 to 0.0265 to get 1.0265

**Finding time:**

Formula: t = I/Pr

Using the same example above, time would be

t = $ 132.50/[$ 5,000*0.09]

= 132.50/$ 450

= 0.2944

We have considered 360 days in a year. Therefore number of days would be,

t = 0.2944 x 360

= 106 days

Finding the interest rate:

Formula: r = I/Pt

Using the same example above, time would be

r = $ 132.50/[$ 5,000*(106/360)]

= 132.50/$ 1,472.22

= 0.09 i.e. 9%

The monthly payment is also figured differently than standard. What is the formula for the monthly payment when using the Banker’s Rule for something like a 30yr mortgage?