Mathematics of Compound Interest

1
Chapter 11

• Mathematics of Compound Interest

2
Compound Interest

• Vn P(1 i)n
• Rule of 72 dividing rate of compound interest
  into 72 yields number of years required for money
  to double
• Compound interest tables are given in Exhibit
  11.2
• Semiannual and other compounding periods

3
Compound Interest

• Vn P ( 1 i/m)nm 1
• Effective annual interest rate
• iE ( 1 i/m)nm - 1

4
Present Value

• Current value of a dollar to be received in the
  future if money currently in hand can be invested
  at a given interest rate
• A dollar to be received in the future is less
  valuable than a dollar in hand today if the
  dollar in hand today is invested
• Present value formula is reciprocal of compound
  interest formula
• PV Vn1/(1r)n

5
Present Value of Annuity

• Annuity series of constant receipts that are
  received at the end of each year for some number
  of years in the future
• Present value of an annuity present value of a
  stream of future cash receipts of a fixed amount
  received at the end of each year for some number
  of years in the future, given a discount rate, r.

6
Present Value of Annuity

• Present value of an annuity factor for n-year
  annuity at discount rate r sum of present value
  factors for each of n years a discount rate r
• Formula for present value of an annuity
• An R ((1 1/(1r)n)/r
• Present value of an annuity factor is given in
  Exhibit 11.4

7
Compound Value of an Annuity

• Compound value of an annuity ending value of a
  series of constant payments made at the end of
  year for a specified number of years that earn
  interest at a given rate per year
• Formula for compound sum of an annuity
• Sn P ((1i)n 1)/i
• Compound value of an annuity answers the
  question, If I invest a constant amount per year
  at the end of each year at a given interest rate,
  what will be the total sum accumulated a the end
  of a given number of years?

8
Application to Personal Decision

• Problem in text of chapter illustrates
  determination of annual savings required to fund
  four-year annuity for childs college education
• First determine lump sum required for four-year
  annuity (PV of an annuity)
• Then determine annual savings over 17 years to
  accumulate the required lump sum