Compound Interest

1
Compound Interest

• Making or Spending Money

2
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
• 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

3
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

4
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
• A is commonly referred to as the accumulated
  value or future value of the account. P is called
  the present value.

5
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

6
Compound Interest

• On-line example
• More on-line examples

7
Compound Interest

• Tutorial

8
Continuous Compounding

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

9
Finding Effective Rate of Interest

• Definition
• Steps for Finding ERI (If a P is not given, use
  100)
• Find the value of the interest compounded
  annually for one year
• Find the value of the interest compounded for the
  given amount of times annually
• Find the interest by subtracting (Step 2
  original principal)
• Divide the answer by the original principal (if
  using 100 dont have to because its already
  written as a percent).

10
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
• Step 3 105.35 100 5.35
• Step 4 5.35

11
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

12
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?

13
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?

14
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?

15
Examples

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

16
Examples

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

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Examples

• On-line problems
• More on-line examples