3 Suppose you are offered the alternative of receiving eithe

3. Suppose you are offered the alternative of receiving either $3000 at the end of five years or P dollars today. There is no question that the $3,000 will be paid in full (no risk). Because you have no current need for the money, you would deposit the P dollars in an account that pays 8% interest. What value of P would make you indifferent to your choice between P dollars today and the promise of $3000 at the end of five years?

Solution

Firstly, determine the present principal amount which is economically equivalent to $3000 in 5 years, given the investment potential of 8% per year.

Amount = Principal (1 + R/100)^T    [Where R = rate of interest and T = time in years. ]

3000 = P (1 + 0.08)⁵

P = 3000 / (1 + 0.08)⁵

P = $ 2042

It is very clear that if P is anything less than $2042, we would prefer the promise of $3000 in 5 years to P dollars today; if P were greater than $2042, you would prefer P. It is less obvious that at a lower interest rate, P must be higher to be equivalent to the future amount. For example, at i = 4%, P = $2466.