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DSC1630 Assignment 01 Semester 01 2022 Solutions
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  • Course
  • DSC1630 - Introductory Financial Mathematics (DSC1630)
  • Institution
  • University Of South Africa (Unisa)

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  • January 21, 2022
  • 21
  • 2021/2022
  • Other
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  • dsc1630
  • dsc
  • dsc1630 2022
  • dsc1630 assignment 1
  • dsc1630 assignment 01
  • an investment of r20 000 accumulated to r45 200 if the applicable simple interest rate is 12 per year
  • then the time under conside

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  • University of South Africa (Unisa)
  • DSC1630 - Introductory Financial Mathematics (DSC1630)
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DSC1630

Introductory Financial Mathematics

Department of Decision Sciences

Assignment 01 for Semester 01 2022

Unique assignment number: 189377
Due Date: 1 March 2022




Question 1

Patric borrows money from Zanele at a simple discount rate of 9,75% per annum. He must
pay him R35 000 in 27 months’ time. The amount of money that he receives from Zanele
now is

[1] R27 321,88.
[2] R44 835,87.
[3] R28 389,51.
[4] R42 678,13.

Answer:

𝑃 is the principal or total amount borrowed (in rand) which is subject to interest (𝑃 is also
known as the present value [𝑃𝑉] of the loan)

𝑟 is the rate of interest, that is, the fraction of the principal that must be paid each period
(say, a year) for the use of the principal (also called the period interest rate)

𝑡 is the time in years, for which the principal is borrowed.

, This is a simple discount calculation as the term discount rate is found in the question. The
formula for simple discount is 𝑃 = 𝑆(1 − 𝑑𝑡).

Given are the future value of the loan (𝑆) which is R35 000, the time period which equals 27
months and the discount rate (𝑑) of 9,75%. The time period that we use must always be in
years.

As the given time is in months we change it to a fraction of a year by dividing the months by
27
the number of months in a year which is 12. Thus 𝑡 = 12
Now we need to determine the present value of the loan. Thus

On a timeline:




𝑆 = 𝑅35 000
27
𝑡=
12
𝑑 = 0,0975

So,

𝑃 = 𝑆(1 − 𝑑𝑡)
27
𝑃 = 35 000 (1 − 0,0975 × )
12
𝑃 = 𝑅27 321,88
Patric receives R27 321,88 from Zanele now.

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