MGFB10_Exam_Questions&Answers_2025.
1. Ryan Shrewdy is planning to retire in 40 years. Currently he has $200,000 of cash
that he can invest right away. His goal is to have $3,000,000 at retirement.
a) NoLoss Investments Management Limited has advised him to invest his cash
($200,000) today into a portfolio of fixed income securities offering 5% annual return. In
addition, they advise Ryan to contribute a constant amount each year for the next 40
years, starting one year from today. Calculate the fixed annual contribution that Ryan
must make for the next 40 years in order to achieve his retirement goal.
a. | | | | | | | | | | |
-200,000 -C -C ................................................................................... ..-C = ?
$3,000,000
Let C = amount need to be saved each year.
FV of $200,000 at 5% in 40 years =$200,000(1.05) 40 = $1,407,997.7424
Shortfall = $3,000,000 – 1,407,997.7424 = $1,592,002.2576
To makeup for the shortfall he needs to save
1+ r t −1
) = $1, 592, 002.2576 (1.05) −1 = $13,178.8513 peryear
40
C = FVA (
r 0.05
b) Ryan has decided to seek the advice of NoRiskNoGain Wealth Managers. Based on
NoRiskNoGains’ advice Ryan has decided to invest the same annual amount (as
calculated in part a) in a well diversified portfolio of Canadian common stocks earning an
annual return of 7%, starting one year from today. In addition, he invests a portion of his
cash savings in Canadian common stocks right away. Any leftover out of his $200,000
cash savings will be invested immediately in real estate earning 6% per year. Ryan’s
objective is to have $3,000,000 in 40 years by investing in Canadian common stocks.
How much can he invest in real estate today? And what will be the value of his real estate
investment in 40 years?
, b. | | | | | | | | | |
-$13,178.8513…................................................................. …-$13,178.8513
PV=? $3,000,000
FVA of $13,178.8513 at 7% per year for 40 years
1.07 40 −1
$13,178.8513 ( ) = $2, 630, 961.4481
0.07
Shortfall = $3,000,000-2,630,961.4481=$369,038.5519
To make up for the shortfall he should invest $369,038.5519/(1.07) 40 = $24,644.5351 from his
cash savings into the well diversified portfolio.
Now he can invest $200,000 – 24,644.5351 = $175,355.4649 in real estate.
His real estate investment after 40 years will worth $175,355.4649(1.06)40 = $1,803,656.85
2. John has just got his undergraduate degree from the UTSC and he is planning for his
career and life in the following 8 years as follows:
1. Right now, he has to work in an accounting firm for a 5-year contract;
2. After he completes this 5-year contract, he will take one year (the 6th year) off and
travel around the world. Fortunately, his travel expense will be fully covered by
his parents.
3. After he comes back from his trip, he will take a two-year MBA program (the 7th
and 8th year) at the Rotman School of Management. The annual tuition fee for this
MBA program is 35,000 dollars. As usual, the annual tuition fee will be paid at
the beginning of each year (at the beginning of the 7th and the 8th year). But this
time, he has to pay for his own tuition fees.
John wants to set up a monthly saving plan in the following 5 years so that he will be able
to pay for his MBA program tuition fees later. The first cash flow of his saving plan will
be made one month from today. The monthly saving plan will provide an annual return of
6%, compounded monthly.
i) What are the effective monthly rate and effective annual rate for John’s saving plan?
Effective monthly rate = 6% /12 = 0.5000%
1. Ryan Shrewdy is planning to retire in 40 years. Currently he has $200,000 of cash
that he can invest right away. His goal is to have $3,000,000 at retirement.
a) NoLoss Investments Management Limited has advised him to invest his cash
($200,000) today into a portfolio of fixed income securities offering 5% annual return. In
addition, they advise Ryan to contribute a constant amount each year for the next 40
years, starting one year from today. Calculate the fixed annual contribution that Ryan
must make for the next 40 years in order to achieve his retirement goal.
a. | | | | | | | | | | |
-200,000 -C -C ................................................................................... ..-C = ?
$3,000,000
Let C = amount need to be saved each year.
FV of $200,000 at 5% in 40 years =$200,000(1.05) 40 = $1,407,997.7424
Shortfall = $3,000,000 – 1,407,997.7424 = $1,592,002.2576
To makeup for the shortfall he needs to save
1+ r t −1
) = $1, 592, 002.2576 (1.05) −1 = $13,178.8513 peryear
40
C = FVA (
r 0.05
b) Ryan has decided to seek the advice of NoRiskNoGain Wealth Managers. Based on
NoRiskNoGains’ advice Ryan has decided to invest the same annual amount (as
calculated in part a) in a well diversified portfolio of Canadian common stocks earning an
annual return of 7%, starting one year from today. In addition, he invests a portion of his
cash savings in Canadian common stocks right away. Any leftover out of his $200,000
cash savings will be invested immediately in real estate earning 6% per year. Ryan’s
objective is to have $3,000,000 in 40 years by investing in Canadian common stocks.
How much can he invest in real estate today? And what will be the value of his real estate
investment in 40 years?
, b. | | | | | | | | | |
-$13,178.8513…................................................................. …-$13,178.8513
PV=? $3,000,000
FVA of $13,178.8513 at 7% per year for 40 years
1.07 40 −1
$13,178.8513 ( ) = $2, 630, 961.4481
0.07
Shortfall = $3,000,000-2,630,961.4481=$369,038.5519
To make up for the shortfall he should invest $369,038.5519/(1.07) 40 = $24,644.5351 from his
cash savings into the well diversified portfolio.
Now he can invest $200,000 – 24,644.5351 = $175,355.4649 in real estate.
His real estate investment after 40 years will worth $175,355.4649(1.06)40 = $1,803,656.85
2. John has just got his undergraduate degree from the UTSC and he is planning for his
career and life in the following 8 years as follows:
1. Right now, he has to work in an accounting firm for a 5-year contract;
2. After he completes this 5-year contract, he will take one year (the 6th year) off and
travel around the world. Fortunately, his travel expense will be fully covered by
his parents.
3. After he comes back from his trip, he will take a two-year MBA program (the 7th
and 8th year) at the Rotman School of Management. The annual tuition fee for this
MBA program is 35,000 dollars. As usual, the annual tuition fee will be paid at
the beginning of each year (at the beginning of the 7th and the 8th year). But this
time, he has to pay for his own tuition fees.
John wants to set up a monthly saving plan in the following 5 years so that he will be able
to pay for his MBA program tuition fees later. The first cash flow of his saving plan will
be made one month from today. The monthly saving plan will provide an annual return of
6%, compounded monthly.
i) What are the effective monthly rate and effective annual rate for John’s saving plan?
Effective monthly rate = 6% /12 = 0.5000%
