Exam (elaborations)
DSC1630 EXAM PACK 2025 {DETAILED QUESTIONS AND ANSWERS}
- Institution
- 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
2ndF CA
Use financial keys
2ndF P/Y 6 ENT ON/C
±25000 PMT
7.5 I/Y
6×6 = N
COMP PV
721181.68 to two decimals is displayed.
[Option 5]
2
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HP10BII and HP10BII+ DSC1630/SOL03/1/2020
C ALL
Questions 2 and 3 are based on the following Use financial keys
situation:
6 P/YR
The Boxing Fund must pay James an old boxer, R18000
every three months indefinitely as compensation. 25000± PMT Money
is worth 11,4% per year, compounded quarterly. 6×6 =N
7.5 I/YR
Question 2 PV
721181.68 to two decimals is displayed.
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
HP10BII and HP10BII+
C ALL
Use normal keys
18000÷ (0.114÷4 )=
The opening balance of the fund is approximately 631578.9474... is displayed.
R631579.
EL-738 and EL-738F
2ndF CA
[Option Use normal keys 4]
18000÷(0.114÷4) = Question 3
631578.9474... is displayed.
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
3
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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:
R631 579 0,1095
12
Now 9 years
4 years
2X 3X
X
Now asked is the size of the payment at year four. Thus we move all the moneys and payments to year
four before we can equate them. Thus move R631579 forward from now until year four, thus four years
forward:
.
Move the payment X forward from now until year four, thus four years forward:
4
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