# Answer to Question #70427 in Finance for Nick Mango

Question #70427
Suppose there are two investors: A and B. Both plan to retire after T years but save for their
retirement in very different ways. Investor A puts $1 into his retirement account at the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does not make any contributions for the first N years, and try to make it up with more contributions at the start of each year for the remaining T −N years, i.e., he will make contributions at t = N, N + 1, . . . , T − 1. (a) Suppose Investor B wants to have the same amount of money as Investor A when both of them retire. What is the annual contribution that Investor B has to make in the remaining T − N years. Express your answer as a function of r, N and T. (b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years. Repeat the same exercise for r = 0.04/year and r = 0.06/year. 1 Expert's answer 2017-10-06T13:25:06-0400 a) The one year spot rate r1: 1,08/(1+r1)=$1018.772/$1000=> r1=6,01% The two year spot rate r2: 1/(1+r2)2=$907,209/$1000=> r2=3,11% The two year spot rate r3:$50*(1+r3)3= $136.967=> r3=40%. b) The one-two year forward rate r0,1: 1,08/(1+r1)=$1018.772/\$1000=> r1=6,01%.
The one-two year forward rate r1,2: 0/(1+r1)+1/(1+r1)(1+r1,2)=0,907209=>r1,2≈4%.
The one-two year forward rate r2,3: 0,4/(1+r1)+0,4/(1+r1)(1+r1,2)+1,4//(1+r1)(1+r1,2)(1+r2,3)= 0,136967=>r2,3=10%.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!