Compound Interest Ross Chapman Brandon Miller Finance 321 Stephen D’Arcy 8:30 AM

 Simple Interest – You only receive interest on your initial investment, meaning every period you take the interest out of your account and the interest grows on the initial investment.  Investment x (1 + t * i) = value after t- years  This is not a very efficient way to invest your money.

Simple Interest Example  Suppose you invest $10,000 in a bank, which pays you simple interest of 12% annually. How much will you have in your bank account after five years?

Simple Interest Solution  $10,000 * (1 + 5 *.12) = $16,000

 Compound Interest – each interest payment is reinvested to earn more interest in subsequent periods. Investment * (1 + i)^ t = Value at time t

Compound Interest Example  Suppose you put $10,000 into a CD at your local bank, at a rate of 12% compounded annually for 5 years. How much will you have when you take out the principle and interest at the end of the 5 years.

Annual interest solution  10,000*(1+.12)^5= $17,623.42

More Compound Interest Sometimes the interest won’t be compounded annually, but rather m times a year.

More Compound Interest  If the interest is convertible m th -ly then The interest rate your money is compounded at is i/m The interest rate your money is compounded at is i/m Investment x (1+i/m)^t*m = Value at time t Investment x (1+i/m)^t*m = Value at time t

More Compound Interest  If you want to know the equivalent annually compounded rate to the interest rate compounded m th -ly  Then use this formula:  i a = ((1+ i/m)^m) - 1

Compound Interest Example  Say you put $10,000 into the bank at 12% convertible monthly for 5 years. How much do you have in your account after 5 year? What is the equivalent annual compounded rate?

Compound Interest Answer  First Question: x (1 +.12/12) ^ 5 *12 =$18, Second Question: i a = ((1 +.12/12) ^ 12) – 1= 12.68%

Continuously Compounded Interest  If you money is compounded continuously that means at all times it’s earning interest.  Principal e rt (Pert)  Equivalent Annual Compounded Rate:  (Accumulate Value/ Investment) ^(1/t) - 1

Continuously Compounded Interest  Say you $10000 in the bank at 12% compounded continuously. How much money do you have after 5 year? What is the equivalent annual compounded rate?

Answer  Accumulated Value:  e (.12)*5 = $18,  Equivalent Annual Compounded Rate: ( /10000) (1/5) -1 = 12.75%

 So as you can see as m increases in size the amount of interest you earn in the year grows.

The End!  Any Question?