Mortgages Analyzed

Simple Interest

# What is Simple Interest?

Simple Interest is a method of interest calculation where the periodic interest is a fixed percentage of the principal amount (original loan amount). Simple Interest is a fixed percentage amount of principal loan amount over a period of time. In case of simple interest, the interest amount is not added to the principal amount to calculate future interest. Therefore, interest does not earn interest.

The concept of simple interest is fundamental to interest calculation and forms the basis of time value of money.

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# Formula for Calculating Simple Interest

## Formula for Simple Interest

Simple Interest is calculated using the formula below.

I = P × r × t

Or,

Interest = Principal × Rate × Time
 P = principal amount (original loan/investment amount) i = interest amount r = annual interest rate (expressed as % per year). Also known as nominal or coupon rate t = time in years (loan term/investment period)

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## Formula for Amount/Ending Balance

The total amount at the end of the loan term is calculated using the formula below.

A = P + I

Or,

Amount = Principal + Interest

Where,

 A = amount/ending balance I = interest amount P = principal amount (original loan/investment amount)

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# Examples

## Example 1: Single Year

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for one year on simple interest at an interest rate of 6% per annum. Principal and interest is payable at the end of the loan term.

Where,

 P = \$100,000 r = 6% t = 1

Interest (I) = 100,000 × 0.06 × 1 = \$6,000

Amount (A) = 100,000 + 6,000 = \$106,000

On Dec 31, 2000, Amit will have to pay \$106,000 which includes an interest amount of \$6,000.

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## Example 2: Multi Year

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for three years on simple interest at an interest rate of 6% per annum. Principal and Interest is payable at the end of the loan term.

Where,

 P = \$100,000 r = 6% t = 3

Interest (I) = 100,000 × 0.06 × 3 = \$18,000

Amount (A) = 100,000 + 18,000 = \$118,000

On Dec 31, 2002, he will have to pay \$118,000 which includes an interest amount of \$18,000.

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## Example 3: Less Than 1 Year

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for three months on simple interest at an interest rate of 6% per annum. Principal and interest is payable at the end of the loan term.

Where,

 P = \$100,000 r = 6% t = 3/12 = 0.25 (time is prorated for the loan term)

Interest (I) = 100,000 × (3/12) × 0.06 = \$1,500

Amount (A) = 100,000 + 1,500 = \$101,500

On Mar 31, 2000, Amit will have to pay \$101,500 which includes an interest amount of \$1,500.

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## Example 4: Daily Interest Rate

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for one year on simple interest at an interest rate of 0.032876712% per day. Principal and interest is payable at the end of the loan term.

Where,

 P = \$100,000 r = 0.032876712% per day t = 365

Interest (I) = 100,000 × 0.00032876712 × 365 = \$12,000

Amount (A) = 100,000 + 12,000 = \$112,000

On Dec 31, 2000, Amit will have to pay \$112,000 which includes an interest amount of \$12,000.

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## Example 5: Monthly Interest Payment

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for 1 year on simple interest at an interest rate of 6% per annum. Interest is payable at the end of each month, while principal is payable at the end of loan term.

Where,

 P = \$100,000 r = 6% t = 1

Monthly Interest (I) = 100,000 × (1/12) × 6% = \$500

Total Interest = 500 × 12 = \$6,000

At the end of each month, Amit will have to pay \$500 per month as interest amount. On Dec 31, 2000, Amit will have to pay \$100,500 which includes \$100,000 principal amount and \$500 which is the monthly payment for the month of December 2000.

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As mentioned earlier, in case of simple interest the interest amount is not added to the principal amount to calculate future interest. Therefore the making the interest payment on periodic (such as monthly) basis or at the end of the period will not make a difference to the total interest amount. However, this is not to say that the cost of loan is the same. The cost of borrowing will be higher if interest payments are made more frequently that just at the end.

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# Calculators

Updated: Feb 18, 2013

The concept of simple interest is fundamental to interest calculation and forms the basis of time value of money
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