Chapter 21Finance: Savings

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Chapter 21-Finance Savings

• How much interest will your savings account earn
  in the next year?
• How much will your balance be on your credit card
  account if you forget to make your payment?
• How much will the payment be on your home
  mortgage?
• How much should you save for retirement?
• How much would you need to save each month to pay
  for a childs college education?
• ? All about money

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Simple Interest

• The method of paying interest in which interest
  is paid only on the original balance.
• Bonds A bond is an obligation to repay a
  specific amount of money at the end of a fixed
  term.
• Example Suppose you bought one of those 30-year
  U.S Treasury bonds for 10,000 that pays a coupon
  rate of 3.375 simple interest. How much
  interest would it earn and what would be the
  total amount after 30 years?

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Simple Interest

• Interest formula I P r t
• Where I interest
• P principal initial balance
• t time (in years)
• r interest rate (APR annual percentage
  rate)
• Total amount A accumulated in the account is
• A P I P Prt P(1rt)
• A P(1rt)
• ? r is always given in percent, but it will be
  converted to decimal form before they are used in
  a formula

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Compound Interest

• 37.
• If at the end of a payment period, the interest
  is paid to the account, then the interest as well
  as the initial balance will earn interest during
  the next payment period. Interest paid on
  interest and original principal is called
  compound interest.
• In compound interest, one must specify the
  compounding period that is, the time elapsing
  before interest is paid.
• ?Compounded annually, semi-annually, quarterly,
  monthly, weekly, daily, etc.
• Example Saving account, Certificate of Deposit
  

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Compound Interest

• Interest formula
• Where P principal initial balance
• n number of compounding periods
• i interest rate per compounding period
• If r is the annual percentage rate, then
• i r/2 when compounded semi-annually
• i r/4 when compounded quarterly
• i r/12 when compounded monthly
• i r/52 when compounded weekly
• i r/365 when compounded daily

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Simple Interest vs Compound Interest

• Suppose you read in the newspaper that one
  investment pays 15 compounded monthly and
  another pays 15.2 compounded semiannually and
  another pays 15.5 simple interest. Which has the
  best return?

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Nominal Rate vs Effective Rate

• A nominal rate is any stated rate of interest for
  a specific length of time. It could be daily
  rate, monthly rate or annual rate (APRannual
  percentage rate)
• The effective rate is the actual percentage rate
  of increase for a length of time, taking into
  account compounding. It equals the simple
  interest rate that would realize exactly as much
  interest over the same period of time. When
  stated per year, it is called effective annual
  rate (EAR), or annual percentage yield (APY) or
  annual equivalent yield

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A Model for Accumulation

• What size deposit do you need to make on a
  regular basis in an account with a fixed rate of
  interest, to have a specified amount at a
  particular time in the future?
• ? Future value of an annuity
• An annuity is a specified number of equal
  periodic payments. Annuities are a common way
  for
• lotteries to pay out grand prizes
• retirees to receive funds saved up to retirement.
• Others planning for a saving in order to make a
  major purchase
• ? Sinking Fund A savings plan to accumulate a
  fixed sum by a particular date. It is a special
  type of annuity.

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Future value of an annuity

• where
• n compounding periods
• i interest rate per compounding period
• A amount accumulated after n periods
• d amount of each deposit at the end of the
  compounding period

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When do we use this formula?

• A fixed amount of deposit is made into an account
  on a regular basis.
• ?Sinking Fund, Retirement Fund
• The Compound Interest formula only gives us the
  amount over time of a single deposited amount.

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Examples

• You save for retirement by contributing the same
  amount each month from your 23rd birthday until
  your 65th birthday, in an account that pays a
  steady 5 annual interest compounded monthly.
• How much will be in your fund at age 65 if you
  save 100 a month?
• How much will be in your fund if you get a steady
  return of 7.5 compounded monthly?

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Homework Assignment

• Skills Check (Page 787)
• 1, 13, 15, 17, 19