OEFENINGEN
ZONDER
OPLOSSING
BEDRIJS-
FINANCIERING
Pauline Delphine Verhelst
VUB | 2019-2020
,Hoofdstuk 5
Oef. 14 pag. 181
Your great-uncle Claude is 82 years old. Over the years, he has accumulated savings of $80,000.
He estimates that he will live another 10 years at the most and wants to spend his savings by
then. (If he lives longer than that, he figures you will be happy to take care of him.)
Uncle Claude places his $80,000 into an account earning 10 percent annually and sets it up in
such a way that he will be making 10 equal annual withdrawals – the first one occurring one
year from now – such that his account balance will be zero at the end of 10 years. How much
will he be able to withdraw each year?
Oef. 32 pag. 183
IRA Investments develops retirement programs for individuals. You are 30 years old and plan
to retire on your 60th birthday. You want to establish a plan with IRA that will require a series
of equal, annual, end-of-year deposits into the retirement account. The first deposit will be made
one year from today on your 31st birthday. The final payment on the account will be made on
your 60th birthday. The retirement plan will allow you to withdraw $120,000 per year for 15
years, with the first withdrawal on your 61st birthday. Also, at the end of the 15th year, you
wish to withdraw an additional $250,000. The retirement account promises to earn 12 percent
annually.
What periodic payment must be made into the account to achieve your retirement objective?
Oef. 34 pag. 184
You are currently 30 years of age. You intend to retire at age 60 and you want to be able to
receive a 20-year, $100,000 beginning-of-year annuity with the first payment to be received on
your 60th birthday. You would like to save enough money over the next 15 years to achieve
your objective; that is, you want to accumulate the necessary funds by your 45th birthday.
a. If you expect your investments to earn 12 percent per year over the next 15 years and
10 percent per year thereafter, how much must you accumulate by the time you reach
age 45?
b. What equal, annual amount must you save at the end of each of the next 15 years to
achieve your objective, assuming that you currently have $10,000 available to meet your
goal? Assume the conditions stated in Part a.
, Oef. 38 pag. 184
Frank Chang is planning for the day when his child, Laura, will go to college. Laura has just
turned eight and plans to enter college on her 18th birthday. She will need $25,000 at the
beginning of each year in school. Frank plans to give Laura a Mercedes-Benz as a
combination graduation and 22nd birthday present. The Mercedes is expected to cost $55,000.
Frank currently has $10,000 saved for Laura. Also, Frank expects to inherit $25,000 nine
years from now that will be used for Laura’s education. Frank expects to be able to earn 7
percent after tax on any investments. How much must Frank save at the end of each of the
next 10 years in order to provide for Laura’s education and the Mercedes?
Oef. 40 pag. 185
Torbet Fish Packing Company wants to accumulate enough money over the next 10 years to
pay for the expected replacement of its digitalized, automated scaling machine. The new
machine is expected to cost $200,000 in 10 years. Torbet currently has $10,000 that it plans
to invest over the next 10 years to help pay for the new machine. Torbet wants to put away
an equal, end-of-year amount into a sinking fund investment account at the end of each of
the next 10 years. Earnings on all of the investments are expected to be 7 percent for the first
five years and 9 percent thereafter. What equal, end-of-year amount must Torbet save each
year over the next 10 years to meet these needs?
Oef. 43 pag. 185
Bobbi Proctor does not want to “gamble” on Social Security taking care of her in retirement.
Hence she wants to begin to plan now for retirement. She has enlisted the services of Hackney
Financial Planning to assist her in meeting her goals. Proctor has determined that she would
like to have a retirement annuity of $200,000 per year, with the first payment to be received
36 years from now at the end of her first year of retirement. She plans a long, enjoyable
retirement of about 25 years. Proctor wishes to save $5,000 at the end of each of the next 15
years, and an unknown, equal end-of-period amount for the remaining 20 years before she
begins her retirement. Hackney has advised Proctor that she can safely assume that all savings
will earn 12 percent per annum until she retires, but only 8 percent thereafter. How much
must Proctor save per year during the 20 years preceding retirement?
ZONDER
OPLOSSING
BEDRIJS-
FINANCIERING
Pauline Delphine Verhelst
VUB | 2019-2020
,Hoofdstuk 5
Oef. 14 pag. 181
Your great-uncle Claude is 82 years old. Over the years, he has accumulated savings of $80,000.
He estimates that he will live another 10 years at the most and wants to spend his savings by
then. (If he lives longer than that, he figures you will be happy to take care of him.)
Uncle Claude places his $80,000 into an account earning 10 percent annually and sets it up in
such a way that he will be making 10 equal annual withdrawals – the first one occurring one
year from now – such that his account balance will be zero at the end of 10 years. How much
will he be able to withdraw each year?
Oef. 32 pag. 183
IRA Investments develops retirement programs for individuals. You are 30 years old and plan
to retire on your 60th birthday. You want to establish a plan with IRA that will require a series
of equal, annual, end-of-year deposits into the retirement account. The first deposit will be made
one year from today on your 31st birthday. The final payment on the account will be made on
your 60th birthday. The retirement plan will allow you to withdraw $120,000 per year for 15
years, with the first withdrawal on your 61st birthday. Also, at the end of the 15th year, you
wish to withdraw an additional $250,000. The retirement account promises to earn 12 percent
annually.
What periodic payment must be made into the account to achieve your retirement objective?
Oef. 34 pag. 184
You are currently 30 years of age. You intend to retire at age 60 and you want to be able to
receive a 20-year, $100,000 beginning-of-year annuity with the first payment to be received on
your 60th birthday. You would like to save enough money over the next 15 years to achieve
your objective; that is, you want to accumulate the necessary funds by your 45th birthday.
a. If you expect your investments to earn 12 percent per year over the next 15 years and
10 percent per year thereafter, how much must you accumulate by the time you reach
age 45?
b. What equal, annual amount must you save at the end of each of the next 15 years to
achieve your objective, assuming that you currently have $10,000 available to meet your
goal? Assume the conditions stated in Part a.
, Oef. 38 pag. 184
Frank Chang is planning for the day when his child, Laura, will go to college. Laura has just
turned eight and plans to enter college on her 18th birthday. She will need $25,000 at the
beginning of each year in school. Frank plans to give Laura a Mercedes-Benz as a
combination graduation and 22nd birthday present. The Mercedes is expected to cost $55,000.
Frank currently has $10,000 saved for Laura. Also, Frank expects to inherit $25,000 nine
years from now that will be used for Laura’s education. Frank expects to be able to earn 7
percent after tax on any investments. How much must Frank save at the end of each of the
next 10 years in order to provide for Laura’s education and the Mercedes?
Oef. 40 pag. 185
Torbet Fish Packing Company wants to accumulate enough money over the next 10 years to
pay for the expected replacement of its digitalized, automated scaling machine. The new
machine is expected to cost $200,000 in 10 years. Torbet currently has $10,000 that it plans
to invest over the next 10 years to help pay for the new machine. Torbet wants to put away
an equal, end-of-year amount into a sinking fund investment account at the end of each of
the next 10 years. Earnings on all of the investments are expected to be 7 percent for the first
five years and 9 percent thereafter. What equal, end-of-year amount must Torbet save each
year over the next 10 years to meet these needs?
Oef. 43 pag. 185
Bobbi Proctor does not want to “gamble” on Social Security taking care of her in retirement.
Hence she wants to begin to plan now for retirement. She has enlisted the services of Hackney
Financial Planning to assist her in meeting her goals. Proctor has determined that she would
like to have a retirement annuity of $200,000 per year, with the first payment to be received
36 years from now at the end of her first year of retirement. She plans a long, enjoyable
retirement of about 25 years. Proctor wishes to save $5,000 at the end of each of the next 15
years, and an unknown, equal end-of-period amount for the remaining 20 years before she
begins her retirement. Hackney has advised Proctor that she can safely assume that all savings
will earn 12 percent per annum until she retires, but only 8 percent thereafter. How much
must Proctor save per year during the 20 years preceding retirement?
