Understanding Interest

Business Economics

Why Interest?

Nothing in this world is free.Banks wouldn’t make moneyPeople wouldn’t make moneyBusinesses wouldn’t make money

Simple Interest

• Interest = prt– P = principal (loan, amount)– R = interest rate– T = time (days, months, years)

– Ordinary interest 360 days– Exact interest 365 days

Example of Simple Interest

• $100 principal• 3% interest rate• 3 years– 100 x .03 x 3– $9 Interest

• If you borrowed the $100, you would now owe $109

• If you loaned someone $100, you would now be due $109

• If you owned something, like a $100 bond, it would be worth $109

Example of Simple Interest

• $500 principal• 5% interest rate• 6 months– $500 x .05 x (6/12)– $12.50 interest

• If you borrowed the $500, you would now owe $512.50

• If you loaned someone $500, you would now be due $512.50

• If you owned something, like a $500 bond, it would be worth $512.50

Compound Interest

• Arises when interest is added to the principal• Interest also earns interest• Interest added to the principal is called

compounding

Example of Compound Interest• Formula• A=P(1+r/n)nt

• P = principal amount (initial amount)

• R = annual rate of interest• T = number of years that amount

is deposited• A = amount of money

accumulated after n years, including interest

• N = number of times the interest is compounded per year

• Initial investment $1,000

• 3% interest• Compounded 4 times

per year (quarterly)• After 4 years

• =$1,000 x (1+0.0075)16

• $1,126.99

2 More Examples

• Initial investment $5,000

• Rate 8%• Compounded monthly• For 5 years• =$5,000

(1+0.00666667)60

• $7,449.23

• Initial investment $300• Rate 5%• Compounded daily• For 3 years• =$300

(1+0.000136986)1095

• $348.55

You Decide….

• Regards of the principal, interest rate, or time, which would you rather have if you were investing money and expecting a return?– Interest compounded quarterly– Interest compounded monthly– Interest compounded daily