Exam (elaborations)
Dsc1630 Assignment 3 Semester 1 2023
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DSC1630/SOL03/S22 Assignment 03 – Detailed Solution
Question 1
An amount of R600 is invested every month for eight years. The applicable interest rate is 14,65% per
year, compounded quarterly. The accumulated amount of these monthly payments is approximately
[1] R57 600.
[2] R107 500.
[3] R108 400.
[4] R109 300.
[5] R321 200.
In this problem we have equal deposits in equal time periods plus the interest rate that is specified is
compounded. Thus we are working with annuities.
The time line is:
R600 R600 ?
0,1465
4
now month 1 month 2 8 years
Given are the monthly payment (R) of R600, the time under consideration t = 8 (in years), the
interest rate jm = 14,65% and the quarterly compounding periods (m = 4). The compounding is
done quarterly and the deposits are monthly. Now, very important is the fact that when working
with annuities the compounding period and payment periods must be the same! If not,
you have to change the compounding period and thus the interest rate to the same period as the
payment periods using the conversion formula in the SG - chapter 3 - see example 3.5. The formula
is as follows: !" #m÷n $
jm
jn = n 1+ −1
m
In this case we firstly need to change the quarterly compounded interest rate to a monthly compound
interest rate using the above formula. After that you can make use of the normal future value
calculation of an annuity S = Rs n i to calculate the accumulated amount S. Now, firstly we convert
the 14,65% compounded quarterly to a compounded monthly rate:
%" # mn &
jm
jn = n 1 + −1
m
%" # 124 &
0,1465
= 12 1 + −1
4
= 0,144747 . . .
4
, DSC1630/SOL03/S2
Secondly, we use the new monthly interest rate to calculate the future value of the annuity:
S = Rs n i
= 600s 8×12 0,144747.../12
= 107 517,439 . . .
The accumulated amount is approximately R107 500.
HP10BII/HP10BII+
EL-738/F/FB C ALL
2ndF CA Use normal and financial keys
Use normal and financial keys Change the interest rate
Change the interest rate 0.1465 ÷ 4 = +1 =
12((1 + 0.1465 ÷ 4) 2ndF y x
yx (4 ÷ 12 )
(4 ÷ 12) − 1) =
= −1 = ×12 =
0.144747 . . . is displayed.
0.144747. . . is displayed.
Store this answer as a percentage in
Store this answer as a percentage in
I/Y and calculate the FV:
I/YR and calculate the FV:
×100 = I/Y
×100 = I/YR
2ndF P/Y 12 ENT ON/C
± 600 PMT 12 P/YR
8 × 12 = N or 8 2ndF ×P/Y N 600 ± PMT
COMP FV 8 × 12 = N or 8 ×P/YR
107 517.4395. . . is displayed. FV
107 517.4395. . . is displayed.
[Option 2]
Question 2
Amy is going to need R145 000 in three years’ time, to pay for a holiday overseas. She immediately
starts to make monthly deposits into an account earning 11,05% interest per year, compounded
monthly. Amy’s monthly deposit is
[1] R3 384,18.
[2] R3 415,34.
[3] R4 027,78.
[4] R4 707,20.
[5] R4 750,55.
5
, DSC1630/SOL03/S2
In this problem we have equal deposits in equal time periods (monthly), plus the interest rate is
specified as compounded monthly. Thus we are working with annuities. As the future value is given
we make use of the future value formula of an annuity. If the payments were at the end of every time
period we would have had an ordinary annuity. But the word immediately indicates an annuity due
instead of an ordinary annuity. As the future value is given the formula to use is S = (1 + i)Rs n i .
The time line is:
R145 000
?R ?R ?R
0,1105
12
now 3 years
Now given are the value she would need or future value S of R145 000, the compound interest rate jm
of 11,05% and monthly compounding periods (m = 12). Asked is the size of her monthly deposits.
Thus
S = (1 + i)Rs n i
" #
0,1105
145 000 = 1+ Rs 3×12 0,1105
12 12
R = 3 384,177 . . .
The size of Amy’s monthly deposits will be R3 384,18.
HP10BII/HP10BII+
EL-738/F/FB C ALL
2ndF CA Use financial keys
Use financial keys Switch the BEG/END mode on
Switch the BGN/END mode on:
BEG/END [on the MAR key]
2ndF BGN/END [on the FV key]
Calculate PMT
Calculate PMT
2ndF P/Y 12 ENT ON/C 12 P/YR
±145 000 FV 145 000± FV
3 × 12 =N 3 × 12 = N
11.05 I/Y 11.05 I/YR
COMP PMT PMT
3 384.177. . . is displayed. 3 384.177. . . to two decimals is dis-
Note: Switch the BGN/END played.
mode off. Press 2ndF BGN/END Note: Switch the BEG/END
mode off. Press BEG/END
[Option 1]
6
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