DSC1630_Self-evaluation
exercises.
, DSC1630
Self-evaluation exercises and solutions
1 Self-evaluation exercises
1.1 Self-evaluation exercise 1
Content: Chapter 2
1. At what simple interest rate must R7 000 be invested for a period
nine of
months to accumulate to
R7 630?
2. Michaelneeds R1 200 urgently.
Peter is prepared to lend him the money on condition that he pays
him R1 295 four months from now.
What simple interest rate is Peter earning on this transaction?
3. How large an amount must be invested on 3 March at a simple interest rate
12%ofper year,to
accumulate to R612 on 2 May of the same year?
4. Mputle Maputle borrows R1 500 on 10 March.
How much interest is he paying if he has to pay back
the loan on 2 July of the same year and a simple interest rate of 21,5% per year is charged on hi
5. How long does it take for an amount of R3 500 to accumulate to R3 755 if simple interest of 18%
year is earned?
6. When will R2 000 invested on 6 March at a simple interest rate of 15% accumulate to R2 240?
7. Sipho borrows money on 31 August and signs an agreement stating that he will pay back the loa
November of the same year.
If the discount rate is 18% per year, and he receives R5 000 on 31 Augu
of the same year, what is the face value of the agreement?
8. What is the equivalent simple interest rate of the previous question?
9. John Drake needs to make the following payments against a loan on his lorry:
R10 000 after six months
R20 000 after one year
R40 000 after two years.
As a result of drought on his farm,
John Drake could not pay the first two
payments.After 18 months, John Drake has a record harvest and immediately makes a down pay
of R50 000 against his loan.
What single size payment should he make two years from now to settle
debt if simple interest of 17% per year is charged on all amounts?
The solutions to these questions are to be found on p 20.
1
,1.2 Self-evaluation exercise 2 DSC1630
1.2 Self-evaluation exercise 2
Content: Chapter 3
1. A deceased had R1 400 in a Swiss bank at the time of hisTwenty
death.years later the beneficiary of
his will learns about the investment and claims
How
it. much must be paid to the beneficiary if the
investment earned 12,5% interest per year compounded half yearly, over the 20 years?
2. How long will it take to save R25 000 for a trip to Europe if you deposit R15 000 into a savings a
now, earning interest of 12% per year, compounded monthly? The initial R15 000 will also be us
pay for the trip.
3. An amount of R1 000 has accumulated to R1 500 after two and a Calculate
half years.the interest rate
per year if interest is compounded monthly.
4. Willem Grobler invests R12 000 at an interest rate of 10,5% per year, compounded
Aftermonthly.
four
years and three months Willem withdraws R15 000 and invests it at 12% interest per year, comp
quarterly.What is the total accumulated amount of both accounts after six years?
5. An investment company invests its funds at an interest rate of 12% per
compounded
year, monthly.
What is the effective interest rate that the company earns?
6. On 3 January Granddad Steyn deposited R2 500 into a savings account for his grandchild who w
born on 26 July the previous year.
Interest is credited at 18,75% per year on the first day
every
of
month.
(a) How much money does his grandchild receive on his first birthday if simple interest is used
odd periods and compound interest for the rest of the term?
(b) How much does he receive if fractional compounding is used for the full period?
7. Joseph would like to buy a lawnmower.
He has three options when it comes to borrowing the R3 750
from the bank:
17,5% per year, compounded semi-annually
16% per year, compounded quarterly
16% per year, compounded monthly
Make use of continuous compounding rates to decide which option Joseph should take.
8. A wholesaler has to pay the following amounts to a manufacturer:
R200 000 after three months
R300 000 after one year and three months
R400 000 after two years.
He would like to reschedule his three payments by making only two paym
The first payment will be made at the end of the first year and the second, twice the size of the
at the end of 21 months.
If interest is calculated at 18,75% compounded quarterly, what is the size
each payment? Use month 21 as the comparison date.
The solutions to these questions are to be found on p 24.
2
, 1.3 Self-evaluation exercise 3 DSC1630
1.3 Self-evaluation exercise 3
Content: Chapters 4 and 5
1. Mr White opened an annuity fund and deposited R3 000 Thereafter
into it. he deposited R500 at the
end of each month into this fund.
Mr Jones, on the other hand, opened his annuity fund by depositing
R5 000 into it. He thereafter deposited R300 at the endeach
of month into this fund.After 15
years of making deposits into the annuity funds, the two friends decided to compare their invest
Calculate the amounts in the two funds after the 15 years if a 12,5% interest rate compounded m
is applicable.
2. An insurance agent offers services to clients who are concerned about their personal financial pl
for retirement.To explain the advantagesanof early start to investing,
she points out that ifthe
25-year-old John starts to save R2 000 at the beginning each
of year for 10 years (and makes no
further contributions) John will
earn more than Jane who waits 10 years and then save R2 000 at
the beginning of each year until retirement at an age of 65 (a total of 30 contributions).
Find the net
earnings (compound amount minus total contributions) of John and JaneAn at annual
age 65.interest
rate of 7% is applicable and the deposits are made at the beginning of each year.
3. A poor student has to repay his study loan of R80 000 which he received when he enrolled for th
time, in equal monthly payments. The repayment will start after he has finished his education in four
years’ time.
Determine his monthly payments if he wants to repay his debt in five years (after stu
for four years) and if interest is calculated at 15% per year, compounded monthly.
4. Determine approximately the accumulated value of R500 payments made every month for a pe
eight years if interest is compounded semi-annually at 13,5% per year.
5. Vusi and Vivian want to purchase a new flat and feel
that they can afford a mortgage payment of
R2 500 a month.They are able to pay R100 000 deposit and obtained a 20-year,
14,75% per annum
mortgage bond (compounded monthly).
(a) How much can they afford to spend on a flat?
(b) After eight years Vusi
receives a huge promotion and decides to buy a much bigger
Whatflat.
equity do they have in their present flat after eight years?
6. Maitland Engineering wants to replace machinery after seven The
years.
company has been investing
a sum of R5 000 in a sinking fund every six months for this The
purpose.
investment has been earning
interest at the rate of
16% per year compounded semi-annually.
Determine the balancethe
of fund
after seven years.
7. A medicalpractitioner ofGauteng buys a holiday home on the west coast with a cash deposit of
R200 000 plus monthly payments R10
of 000 for a period of
five years.Interest is 12% per annum
compounded monthly.Calculate the cash price of the house.
The solutions to these questions are to be found on p 29.
3
exercises.
, DSC1630
Self-evaluation exercises and solutions
1 Self-evaluation exercises
1.1 Self-evaluation exercise 1
Content: Chapter 2
1. At what simple interest rate must R7 000 be invested for a period
nine of
months to accumulate to
R7 630?
2. Michaelneeds R1 200 urgently.
Peter is prepared to lend him the money on condition that he pays
him R1 295 four months from now.
What simple interest rate is Peter earning on this transaction?
3. How large an amount must be invested on 3 March at a simple interest rate
12%ofper year,to
accumulate to R612 on 2 May of the same year?
4. Mputle Maputle borrows R1 500 on 10 March.
How much interest is he paying if he has to pay back
the loan on 2 July of the same year and a simple interest rate of 21,5% per year is charged on hi
5. How long does it take for an amount of R3 500 to accumulate to R3 755 if simple interest of 18%
year is earned?
6. When will R2 000 invested on 6 March at a simple interest rate of 15% accumulate to R2 240?
7. Sipho borrows money on 31 August and signs an agreement stating that he will pay back the loa
November of the same year.
If the discount rate is 18% per year, and he receives R5 000 on 31 Augu
of the same year, what is the face value of the agreement?
8. What is the equivalent simple interest rate of the previous question?
9. John Drake needs to make the following payments against a loan on his lorry:
R10 000 after six months
R20 000 after one year
R40 000 after two years.
As a result of drought on his farm,
John Drake could not pay the first two
payments.After 18 months, John Drake has a record harvest and immediately makes a down pay
of R50 000 against his loan.
What single size payment should he make two years from now to settle
debt if simple interest of 17% per year is charged on all amounts?
The solutions to these questions are to be found on p 20.
1
,1.2 Self-evaluation exercise 2 DSC1630
1.2 Self-evaluation exercise 2
Content: Chapter 3
1. A deceased had R1 400 in a Swiss bank at the time of hisTwenty
death.years later the beneficiary of
his will learns about the investment and claims
How
it. much must be paid to the beneficiary if the
investment earned 12,5% interest per year compounded half yearly, over the 20 years?
2. How long will it take to save R25 000 for a trip to Europe if you deposit R15 000 into a savings a
now, earning interest of 12% per year, compounded monthly? The initial R15 000 will also be us
pay for the trip.
3. An amount of R1 000 has accumulated to R1 500 after two and a Calculate
half years.the interest rate
per year if interest is compounded monthly.
4. Willem Grobler invests R12 000 at an interest rate of 10,5% per year, compounded
Aftermonthly.
four
years and three months Willem withdraws R15 000 and invests it at 12% interest per year, comp
quarterly.What is the total accumulated amount of both accounts after six years?
5. An investment company invests its funds at an interest rate of 12% per
compounded
year, monthly.
What is the effective interest rate that the company earns?
6. On 3 January Granddad Steyn deposited R2 500 into a savings account for his grandchild who w
born on 26 July the previous year.
Interest is credited at 18,75% per year on the first day
every
of
month.
(a) How much money does his grandchild receive on his first birthday if simple interest is used
odd periods and compound interest for the rest of the term?
(b) How much does he receive if fractional compounding is used for the full period?
7. Joseph would like to buy a lawnmower.
He has three options when it comes to borrowing the R3 750
from the bank:
17,5% per year, compounded semi-annually
16% per year, compounded quarterly
16% per year, compounded monthly
Make use of continuous compounding rates to decide which option Joseph should take.
8. A wholesaler has to pay the following amounts to a manufacturer:
R200 000 after three months
R300 000 after one year and three months
R400 000 after two years.
He would like to reschedule his three payments by making only two paym
The first payment will be made at the end of the first year and the second, twice the size of the
at the end of 21 months.
If interest is calculated at 18,75% compounded quarterly, what is the size
each payment? Use month 21 as the comparison date.
The solutions to these questions are to be found on p 24.
2
, 1.3 Self-evaluation exercise 3 DSC1630
1.3 Self-evaluation exercise 3
Content: Chapters 4 and 5
1. Mr White opened an annuity fund and deposited R3 000 Thereafter
into it. he deposited R500 at the
end of each month into this fund.
Mr Jones, on the other hand, opened his annuity fund by depositing
R5 000 into it. He thereafter deposited R300 at the endeach
of month into this fund.After 15
years of making deposits into the annuity funds, the two friends decided to compare their invest
Calculate the amounts in the two funds after the 15 years if a 12,5% interest rate compounded m
is applicable.
2. An insurance agent offers services to clients who are concerned about their personal financial pl
for retirement.To explain the advantagesanof early start to investing,
she points out that ifthe
25-year-old John starts to save R2 000 at the beginning each
of year for 10 years (and makes no
further contributions) John will
earn more than Jane who waits 10 years and then save R2 000 at
the beginning of each year until retirement at an age of 65 (a total of 30 contributions).
Find the net
earnings (compound amount minus total contributions) of John and JaneAn at annual
age 65.interest
rate of 7% is applicable and the deposits are made at the beginning of each year.
3. A poor student has to repay his study loan of R80 000 which he received when he enrolled for th
time, in equal monthly payments. The repayment will start after he has finished his education in four
years’ time.
Determine his monthly payments if he wants to repay his debt in five years (after stu
for four years) and if interest is calculated at 15% per year, compounded monthly.
4. Determine approximately the accumulated value of R500 payments made every month for a pe
eight years if interest is compounded semi-annually at 13,5% per year.
5. Vusi and Vivian want to purchase a new flat and feel
that they can afford a mortgage payment of
R2 500 a month.They are able to pay R100 000 deposit and obtained a 20-year,
14,75% per annum
mortgage bond (compounded monthly).
(a) How much can they afford to spend on a flat?
(b) After eight years Vusi
receives a huge promotion and decides to buy a much bigger
Whatflat.
equity do they have in their present flat after eight years?
6. Maitland Engineering wants to replace machinery after seven The
years.
company has been investing
a sum of R5 000 in a sinking fund every six months for this The
purpose.
investment has been earning
interest at the rate of
16% per year compounded semi-annually.
Determine the balancethe
of fund
after seven years.
7. A medicalpractitioner ofGauteng buys a holiday home on the west coast with a cash deposit of
R200 000 plus monthly payments R10
of 000 for a period of
five years.Interest is 12% per annum
compounded monthly.Calculate the cash price of the house.
The solutions to these questions are to be found on p 29.
3
