lecture_chap05_06A

If the interest rate is 1 then how much can you

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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.

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