Economics

This tutorial problem set is the rst part of assignment 1. Four tutorials will be collected
and marked and the best three marks will count for the assignment.
1. Feasible lifetime consumption plans under certainty
Please show all working.
Q1. (1 mark) Beth is 25 years old today, and will retire on her 60th birthday. Suppose
she saves $5,000 into a retirement account each year at the end of the year, and receives
an interest rate of 3% with yearly compounding. How much will Beth’s retirement
account have in it on the day she retires? Hint: Use the formula for the future value of
savings from the lecture to help solve this problem.
Q2. (1 mark) If Beth lives to be age 80, how much can she spend each year in retirement
without running out of money before she dies?
Q3. (1 mark) Arnold is 25 years old today, and will retire on his 65th birthday and die
on his 90th birthday. Suppose he has a xed yearly income of $40,000 and he receives
an interest rate of 2.5% with yearly compounding. Arnold saves and consumes at the
end of each year. If Arnold saves $5,000 into a retirement account each year, how much
will Arnold’s retirement account have in it the day he retires?
Q4. (1 mark) What replacement rate will Arnold’s saving plan achieve?
Q5. (1 mark) What percentage of his income should he save if he wants 70% salary
replacement rate after he retires?
Q6. (1 mark) Arnold suddenly decides to cut back on work in the two years before
retirement and as a result he does not add to his savings for those two years, but he
keeps consuming $35,000 p.a. What will his his feasible annual consumption amount
during retirement be now?
Q7. (1 mark) Now suppose that in
ation is 2% p.a. Arnold’s wage of $40,000 increases
at the rate of in
ation, and he receives a nominal interest rate of 4.5% p.a. on his
savings. Arnold still wants to save $5,000 each year in real terms. Show that if Arnold
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2 25005 ECONOMICS AND FINANCE OF THE LIFECYCLE: PROBLEM SET 2
also increases his savings at the in
ation rate of 2% each year, the real value of his
retirement account is the same as for Q4.
2. Simulation exercise: sequencing risk
Q9. (3 marks) (Milevsky 2006) Build an excel spreadsheet that models the next 60 years
of your life. Assume that you save $1 (S = 1) real each year during 30 years of work and
that you spend $8 (C = 8) real each year during 30 years of retirement. Generate ten
sequences of 60 random returns that are normally distributed with an average return of
8% p.a. and a standard deviation of 15%. Hint: You can generate a normal random
rate of return in excel using =NORMINV(RAND(),8,15)". The random numbers will
change every time the spreadsheet recalculates. To stop this you can set recalculation to
`manual’ under the Formulas/Calculation Options tab.
Using the formula in your lecture notes, compute the Discounted Present Value of the
Life Cycle Plan (DVLP) for each returns sequence.
Compute the average and standard deviation of the DVLP over these ten sequences.
For the sequences that result in a negative DVLP, identify precisely the year in which
you ran out of money.

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