Question

Your wealthy uncle wants to donate money to you so that you can pursue your hobbies without fulltime employment. If given a choice between the following four income streams, which would you prefer assuming an interest rate of 5% p.a.?

(a) $400,000 today

(b) $15,000 per year forever

(c) $30,000 each year for the next 20 years

(d) $600,000 in 10 years’ time

Attention tutor: please respond comprehensively addressing four income streams. Please use only formulas, without using excel. Please provide clear answers and detailed answers.

Answer 1

Calculating present worth of each alternative to compare them

Alternative a). Present worth = $400000

Alternative b). present value of a forever annuity is Annual payment/interest rate

So, present worth = 15000/0.05 = $300000

Alternative c). Present value of an annuity that pay at the end of each year for next 20 years is

PV = PMT*(1 - (1+r)^(-t))/r = 30000*(1 - 1.05^-20)/0.05 = $373866.31

So, present worth = $373866.31

Alternative d). Present value of a future payment is calculated using formula

PV = FV/(1+r)^t = 600000/1.05^10 = $368347.95

Present worth = $368347.95

From the present values, we can see that present value of alternative a is maximum, so this should be opted.