understanding interest business economics. why interest? nothing in this world is free. banks...

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