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Chapter 2: Factors Affecting Retirement Planning
1. What is longevity? Why does it matter in the retirement planning process? (pg 56)
Longevity - retirees need to plan for life to avoid outliving assets
o women have longer expectancy than men = greater risk not having
enough to live on in retirement
o ppl live longer b/c:
• better health care system
• advances in medical tech
• better nutrition
• emphasis on exercise
2. What is the probability of: (pg 56)
a) a 60 yr old man living to age 85?
o 31%
b) a 65 yr old man living to age 85? Note: These answers are different because
some men die between the ages of 60 to 65. To reach the age of 85, a 60 yr old
man must 1st live to age 65.
o 33%
c) a 60 yr old woman living to age 80?
o 69%
d) a 65 yr old woman living to age 80?
o 71%
3. What is the value in 30 yrs of $50,000 in 2008 dollars, if inflation is 2.5%? What is the
amount in 30 yrs of $50,000 in $2038 if inflation is 2.5%?
Value = 50,000
Amount = FV = ? = 104,878.379
o n = 30
o PV = 50,000
o I% = 2.5% Chapter 2: Factors Affecting Retirement Planning
4. Jill will be receiving a pension at retirement of $35,000 a yr. She expects to live to collect
this pension for 30 yrs. The nominal discount rate is 7% and the inflation is expected to
be 2%.
a) What is the real discount rate?
o k real(1 + nominal rate/ 1 + inflation rate) - 1 = (1.07/1.02) -1 = 4.902%
b) What is the PV at retirement of her pension if it is:
i. Indexed = w/ real interest rate?
• n = 30
• I% = 4.902%
• PMT = 35000
• PV =? = 570,772.9413
• BGN mode
ii. Not indexed = w/ nominal rate?
• n = 30
• I% = 7%
• PMT = 35000
• PV = ? = 464,718.59
• BGN mode
5. What is bracket creep?
no inflation adj to tax brackets --> average and marginal tax rates increase
tax brackets go up by more than inflation
salary increases due to inflation, their average and marginal tax rates will both
gradually "creep up"
impact: gradual impairment of one's purchasing power due to increased tax bill
not occur if govt increase the tax rates by, at least, the rate of inflation
6. Alice earned 9.2% on her RRSP investments this yr and inflation was 3.5%. Her
investments are worth $150,000 and she wants to retire in 12 yrs. Chapter 2: Factors Affecting Retirement Planning
a) What is the future value of her investment at the nominal rate of return?
o n = 12
o I% = 9.2%
o PV = 150,000
o FV =? = 431,283.5757
b) What is the future value of her investments at the real rate of return?
o real rate = (1 + nom/ 1 + inflation) -1 = (1.092/1.035) - 1 = 5.507 = I%
o n = 12
o PV = 150,000
o FV =? = 285,416.255
c) What is the value of part (b) if you add inflation back into the future value?
o Val = 431,283.5757 b/c nominal not include inflation
7. Marshall's Guaranteed Investment Certificate is earning 3% before tax and his marginal
tax rate is 44%. (pg 64)
a) What is his after tax rate of return?
o After tax rate of return = (I%)(1 -T)
= (0.03)(1 - 0.44)
= 1.68%
b) If inflation is 2%, what is his real rate of return:
i. before tax?
• real rate = (1 + nom/ 1 + inflation) - 1 = (1.03/1.02) -1 = 0.9803%
ii. after tax?
• k real,AT(1 + knom1 - T))/(1 + i)] - 1
= (1 + 0.03(1 - 0.44))/(1.02)] - 1
= - 0.3137%
8. Mary earned 8% before tax on her investment. If her marginal tax rate is 44%, what is
her after tax return if her income was: (pg 64) Chapter 2: Factors Affecting Retirement Planning
a) Interest income
o Interest income = (I%)(1 -T)
= (0.08)(1 - 0.44)
= 4.48%
b) Capital gain
o Capital gain tax = Capital gain - [(Capital gain)(50%)(marginal tax)]
= 0.08 - [(0.08)(0.5)(0.44)]
= 6.24%
c) If inflation is 2.5%, what is her real return after tax for the interest income and
capital gain?
o Interest income k = [(1 + (I%)(1 -T))/(1 + inflation)] - 1
real
= [(1 + (0.08)(1 - 0.44))/(1.025)] - 1
= 1.93%
o Capital gain kreal(1 + nom/1 + inflation) -1
= (1.0624/1.025) - 1
= 3.648%
9. Al earned 9.2% on his RRSP investments this yr. He just read in the paper that inflation
was 1.7% for the yr ended March 31, 2008. His goal was to earn a 7.5% real rate of
return.
a) What is Al's real rate of return
o real rate of return = (1 + nom/ 1 + inflation) -1
= (1.092/1.017) -1
= 7.37%
b) What should his rate of return have been?
o goal: 0.075 = (1 + nom/ 1 + inflation) -1
(0.075 + 1) = (1.017) = 1 + nom
nom = 9.327% Chapter 2: Factors Affecting Retirement Planning
c) What would Al's real rate of return have been if inflation had been 4.2%?
o real rate = (1 + nom/ 1 + inflation) -1
= (1.092/1.042) -1
= 4.79%
d) If inflation is 4.7%, what rate of return did Al need to achieve to have a 7.5% real
rate of return?
o 0.075 = (1 + nom/ 1 + 0.047) -1
nom = 12.55%
10. Bonnie has $10,000 in an RRSP earning 8% interes

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