Exam (elaborations)
DSC1630 EXAM PACK 2025 {DETAILED QUESTIONS AND ANSWERS }
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- University Of South Africa
DSC1630 EXAM PACK 2025 {DETAILED QUESTIONS AND ANSWERS }
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Question 1
Mabe borrowed an amount of money from his father. The loan will be paid back by means
of payments of R25000 each every second month for six years. An interest rate of 7,5% per
year, compounded every two months, will be applicable. The amount of the loan is
[1] R900000,00.
[2] R1127887,64.
[3] R400738,72.
[4] R238067,35. [5] R721181,68.
In this problem we have equal payments in equal time periods plus the interest rate that is
specified is compounded. Thus we are working with annuities. As the payments are not
specified as being paid at the beginning of the period we assume them as being paid at the
end of each time period. We thus have to calculate the present value of an ordinary annuity
or P = Ra n i. Now given is the payments of R25000, the interest rate of 7,5% compounded
every two months, thus m = 6, and the time period t as 6 years. The time line is:
R25 000 R25 000
?
6 years
Now
P = Ra n i
P = 25000a6×6
0,075/6 =
721181,684...
The present value of the loan is R721181,68.
EL-738 and EL-738F HP10BII and HP10BII+
2ndF CA C ALL
Use financial keys Use financial keys
2ndF P/Y 6 ENT ON/C 6 P/YR
±25000 PMT 25000± PMT
7.5 I/Y 6×6 =N
6×6 = N 7.5 I/YR
COMP PV PV
2
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, lOMoAR cPSD| 47715245
DSC1630/SOL03/1/2020
721181.68 to two decimals
721181.68
is to two decimals is
displayed. displayed.
[Option 5]
Questions 2 and 3 are based on the following situation:
The Boxing Fund must pay James an old boxer, R18000 every three months indefinitely as
compensation. Money is worth 11,4% per year, compounded quarterly.
Question 2
The opening balance of this fund is approximately
[1] R474536.
[2] R157895.
[3] R1105351.
[4] R631579.
[5] none of the above.
This is annuity calculation as there are equal payments in equal time periods as well as a
given compound interest rate. But the payments are being made for an indefinite period thus
we have a perpetuity. The present value of a perpetuity can be calculated as where
as the interest is compounded.
Given is the interest rate of 11,4% per year, compounded quarterly, thus . The
payments are given as R18000 every three months thus R = 18000. We need to calculate the
present value of the fund P. Thus
The opening balance of the fund is approximately R631579.
3
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, lOMoAR cPSD| 47715245
DSC1630/SOL03/1/2020
EL-738 and EL-738F HP10BII and HP10BII+
2ndF CA C ALL
Use normal keys Use normal keys
18000÷(0.114÷4) = 18000÷ (0.114÷4 )=
631578.9474... is displayed.
631578.9474... is displayed.
[Option 4]
Question 3
James asks to reschedule the compensation in three payments, the first payment now, the
second payment twice the size of the first payment four years from now, and the third
payment three times the size of the first payment nine years from now. The Boxing Fund
agrees on condition that the interest rate changes to 10,95% per year, compounded monthly.
The amount to the nearest hundred rand that James can expect to receive four years from
now is
[1] R864000.
[2] R184800. [3] R369600. [4]
R557510.
[5] none of the above.
This is a compound interest calculation as the term compounded is found in the question.
The formula for compound interest calculations is
.
In this question the person is rescheduling his compensation payments paid to him. Weaver
want to split his total compensation of R631579, calculated in Question 2, into three
payments. Now what they owe him they must pay him thus
the total of compensation = total of all the payments.
But you cannot add values at different time periods together. You must first move them to
the same date namely the one that is asked namely year four.
First we draw a time line of the problem:
4
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