Compound Interest

COMPOUND INTEREST
Making or Spending Money

SIMPLE INTEREST FORMULA


If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, then interest I charged is

I  Pr t



This interest is not used very often. Interest is usually compounded which means interest is charged or given on the interest and the principal. 

Simple Interest Example

COMPOUND INTEREST
Payment Periods:
 Annually
Once per year
 Semiannually
Twice per year
 Quarterly
Four times per year
 Monthly
Twelve times per year
 Weekly
Fifty two times per year
 Daily
365 (360 by banks) per year


COMPOUND INTEREST FORMULA


The amount A after t years due to a principal
P invested at an annual interest rate r compounded n times per year is



r
A  P  1  n 


nt

A is commonly referred to as the accumulated value or future value of the account. P is called the present value.

COMPOUND INTEREST
Example:
 Investing $1000 at an annual rate of 8% compounded annually, quarterly, monthly, and daily will yield the following amounts after 1 year:
 Annually
 Quarterly
 Monthly
 Daily


COMPOUND INTEREST


On-line example

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COMPOUND INTEREST


Tutorial

Continuous Compounding
 The

amount A after t years due to a principal P invested at an annual interest rate r compounded continuously is

A  Pe

rt

FINDING EFFECTIVE RATE OF
INTEREST


Definition

Steps for Finding ERI: (If a P is not given, use
$100)
1. Find the value of the interest compounded annually for one year
2. Find the value of the interest compounded for the given amount of times annually
3. Find the interest by subtracting (Step 2 – original principal) 4. Divide the answer by the original principal (if using 100 don’t have to because it’s already written as a percent).


EFFECTIVE RATE OF INTEREST
Finding Interest Video
 What is the Effective Rate of Interest for
5.25% compounded quarterly?
 Step 1: 100(1 + .0525)(1) = A
 A = 105.25




Step 2: 100  1 

.0525

4


 105.35

4

Step 3: 105.35 – 100 = 5.35
 Step 4: 5.35%


PRESENT VALUE FORMULAS


The present value P of A dollars to be received after t years, assuming a per annum interest rate r compounded n times per year, is 

 nt

r
P  A 1  n 
If the interest is compounded continuously, then
P  Ae  rt

EXAMPLES


Sears charges 1.25% per month on the unpaid balance for customers with charge accounts (interest is compounded monthly).
A customer charges $200 and does not pay her bill for 6 months. What is the bill at that time? EXAMPLES


Tracy is contemplating the purchase of 100 shares of stock selling for $15 per share. The stock pays no dividends. Her broker says that the stock will be worth $20 per share in 2 years. What is the annual rate of return on this investment?

EXAMPLES


Will invests $2000 in a bond trust that pays
9% interest compounded semiannually. His friend Henry invests $2000 in a certificate of deposit (CD) that pays 8.5% compounded continuously. Who has more money after 20 years, Will or Henry?

EXAMPLES


How long will it take for an investment to double in value if it earns 5% compounded continuously? EXAMPLES


What annual rate of interest compounded annually should you seek if you want to double your investment in 5 years?

EXAMPLES
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On-line problems

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