Exam (elaborations) DSC1630 - Introductory Financial Mathematics (DSC1520)

BASIC SOLUTIONS FOR DSC1630 EXAMINATION QUES-
TION PAPER OCT/NOV 2012
1. Identification: Simple interest rate

R9 000 R10 000

11,5%
2 months now 10 months


Savings worth at month 10 – move R9 000 from 2 month’s ago to 10 month’s in future:



S = P (1 + rt)
 
12
= 9 000 1 + 0,115 ×
12
= 9 000(1,115 . . .)
= R10 035,00.

Money Short:
R10 035,00 − R10 500 = −465,00
She shorts R465,00.
Option [3]

2. Identification: Simple discount rate


d = 0,18

31 Aug 2 Nov
R5 000
t = day number 306 - day number 243 = 63 days




P = S(1 − dt)
 
63
5 000 = S 1 − 0,18 ×
365
5 000
63

=S
1 − 0,18 × 365
S = R5 160,32.

Option [2]
1

, 3. Identification: Compound interest

jm = 12%
m = 12
P =P
S = 2P
t=?
 tm
jm
S = P 1+
m
0,12 t12
2P = P (1 + )
12
 12t
2P 0,12
= 1+
P 12
 
0,12
ln 2 = 12t ln 1 +
12
ln 2

= 12t
ln 1 + 0,12
12
 
ln 2
ln(1+ 0,12 )
t= 12

12
t = 5,80506 years
t ≈ 5,81.

Option [1]

4. Identification: Odd periodes – method given

R375 000
10,45%/12 27 days
25 days Full=7 months odd
odd

7 March 1 April 1 May 1 June 1 July 1 Aug 1 Sept 1 Oct 1 Nov 28 Nov




S = P (1 + rt)(1 + r)t (1 + rt)
   7 × 12  
25 0,1045 12 1 27
= 375 000 1 + 0,1045 × 1+ 1+ × 0,1045
365 12 365
= 404 419,5870 . . .
≈ R404 419,59.

Option [4]


2