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.
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.
