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Unformatted text preview: ties and Perpetuities 6.2
• Annuity – finite series of equal payments
that occur at regular intervals
• If the first payment occurs at the end of the
period, it is called an ordinary annuity
• If the first payment occurs at the beginning of
the period, it is called an annuity due • Perpetuity – infinite series of equal
payments Annuities and Perpetuities –
Basic Formulas
• Perpetuity: PV = C / r
• C is the amount of the regular payments. This
variable is referred to as PMT in the calculator
context • Annuities: 1 1 − 1 + )t
(
r
PV = C
r 1 + )t − (
r
1
FV = C r Annuities and the Calculator
• You can use the PMT key on the calculator
for the equal payment
• The sign convention still holds
• Ordinary annuity versus annuity due
• Most problems are ordinary annuities and this
is the default. (Payments are at the end.)
• For annuity due calculations, reset the
calculator to BEGIN. Annuity – Example 1
• You will make loan payments of $632 per
year for 48 years. If the interest rate is 1%,
then how much can you borrow? Annuity – Example 1 continued
• You borrow money TODAY so you need to
compute the present value.
• Formula Approach
1 1 − (1.01) 48
PV = 632 .01 = 23,999.54 • Calculator Approach
• 48 N; 1 I/Y; 632 PMT; CPT PV = 23,999.54
($24,000) Annuity – Sweepstakes Example
• Suppose you win the Publishers
Clearinghouse $10 million sweepstakes.
The money is paid in equal annual
installments of $333,333.33 over 30 years.
If the appropriate discount rate is 5%, how
much is the sweepstakes actually worth
today?
• Formula Approach
• PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29
• Calculator Approach
• 30 N; 5 I/Y; 333,333.33 PMT; CPT PV = 5,124,150.29 Workshop #6
• You want to receive $50,000 per year in
retirement. If you can earn 7.5% per year and
you expect to need the income for 25 years, how
much do you need to have in your account at
retirement?
• Answer:
• Calculator: PMT = 50000; N = 25; I/Y = 7.5; CPT
PV = 557,347
• Form...
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This document was uploaded on 02/06/2014.
 Fall '14

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