Explanation A perpetuity is an annuity in which the payments go on forever. Use the formula for the present value of an ordinary annuity: P = R [ 1 − ( 1 + i ) − n i ] Here, P is the present value, R is the periodic payment, i is the interest rate per period, and n is the number of periods. Observe the changes in the value of P when n gets larger and larger for a given value of R and i . For example, take R = $ 50 , 000 , i = 5 % = 0.05 , and n = 5 to obtainthe value of P as follows: P ( n = 5 ) = 50 , 000 [ 1 − ( 1 + 0.05 ) − 5 0.05 ] = 1 , 000 , 000 [ 1 − 0.7835261 ] = 1 , 000 , 000 × 0.2164738 = 216 , 473.83 Increase the value of n to 10: P ( n = 10 ) = 50 , 000 [ 1 − ( 1 + 0.05 ) − 10 0.05 ] = 1 , 000 , 000 [ 1 − 0.613913 ⋯ ] = 1 , 000 , 000 × 0.386086 ⋯ = 386 , 086.75 For n = 20 , the present value will be as follows: P ( n = 20 ) = 50 , 000 [ 1 − ( 1 + 0.05 ) − 20 0.05 ] = 1 , 000 , 000 [ 1 − 0.376889 ] = 1 , 000 , 000 × 0

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 5.3, Problem 56E

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Chapter 5.3, Problem 55E

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Finite Mathematics (11th Edition)

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Why the present value of perpetuity is given by P = R i ?

Solution Summary: The author explains that a perpetuity is an annuity in which the payments go on forever.

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Chapter 5 Solutions