6. Section 2.3 #9 Suppose that you pay $1,000 at time 0, get $4,000 at time 1, a

Question

6. Section 2.3 #9 Suppose that you pay $1,000 at time 0, get $4,000 at time 1, and pay $2,000 at time 2. Let Co $1,000, C1$4,000, and C2-$2, 000. Set C CoC C2 - $1,000 _ $4,000+ $2,000 =-$1,000. Find T such that getting an inflow of-C at time T has the same present value as the above sequence of financial transactions, assuming that the growth of money is governed by compound interest at i = 1%. Show that T is greater than the weighted average T = + + 2. This shows that Inequality (2.3.11) need not hold if you have a negative contribution.]

Explanation / Answer

-1000+4000/(1+1%)^1-2000/(1+1%)^2=1000/(1+1%)^T

=>999.803=1000/(1+1%)^T

=>T=log(1000/999.803)/log(1.01)

=>T=0.02

WEIGHTED AVERAGE=(1000)/(-1000)*0+(-4000)/(-1000)*1+(2000)/(-1000)*2=0

SO T IS GREATER THAN WEIGHTED AVERAGE

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