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EXAMPLE 34.14 : For a formula of y = [ 1 - 1 / (1 + r) ^ n ] / r, let y = present value, r = interest rate / year, n = number of years to future value of 1 : (a) Find a simple mathematical relationship of y as a function of r when n = 1 million years. (b) What is the present value of $10000, if the annual discount rate is 10 %, forever?
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Answer Posted / kangchuentat
(a) When n = 1 million years, it could be approximated as n = infinity. Then y = [ 1 - 1 / (1 + r) ^ n ] / r = [ 1 - 1 / (1 + r) ^ (infinity) ] / r = [ 1 - 1 / (infinity) ] / r = (1 - 0) / r = 1 / r. (b) For future value of $10000 and n = infinity forever, use the equation of y = 1 / r for future value of 1 and interest rate r. As r = 10 % = 0.1, then y = x / r = $10000 / 0.1 = $100000, where x = future value. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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