Antwoorde / Answers 1
1.1
P = R 31 450, r = 3,5 % , n = 5 jaar / years
I = Pnr
3,5
= R 31 450 X ──── X 5
100
= R 5 509,75
a = R 5 509,75
[ 1. ]
A = P + I
= R 31 450 + R 5 509,75
= R 36 953,75
b = R 36 953,75
[ 1. ]
1.3
P = R 1 250, r = 5,5 % , n = 2 jaar / years
I = Pnr
5,5
= R 1 250 X ──── X 2
100
= R 137,50
e = R 137,50
[ 1. ]
A = P + I
= R 1 250 + R 137,50
= R 1 387,50
f = R 1 387,50
[ 1. ]
1.5
P = R 12 500, r = 25,2 % , n = 5 jaar / years
I = Pnr
25,2
= R 12 500 X ──── X 5
100
= R 15 750
k = R 15 750
[ 1. ]
A = P + I
= R 12 500 + R 15 750
= R 28 250
m = R 28 250
[ 1. ]
1.7
A = R 7 874, r = 6 % ,
I = A ─ P
= R 7 874 ─ R 6 350
= R 1 524
q = R 1 524
[ 1. ]
Pnr = I
6
R 12 500 X ──── X n = R 1 524
100
381 X n = 1 524
1 524
n = ────
381
= 4
r = 4
[ 1. ]
1.9
A = R 924, r = 5 % , P = R 840
I = A ─ P
= R 924 ─ R 840
= R 84
u = R 84
[ 1. ]
Pnr = I
5
R 840 X ──── X n = R 84
100
42 X n = 84
84
n = ────
42
= 2
v = 2
[ 1. ]
1.11
A = R 5 624, P = R 3 800, n = 4 jaar / years
I = A ─ P
= R 5 624 ─ R 3 800
= R 1 824
y = R 1 824
[ 1. ]
Pnr = I
r
R 3 800 X ──── X 4 = R 1 824
100
152 X r = 1 824
1 824
r = ────
152
= 12
z = 12 %
[ 1. ]
1.13
A = R 221 450, I = R 6 450, r = 6 %
P = A ─ I
= R 221 450 ─ R 6 450
= R 215 000
cc = R 215 000
[ 1. ]
Pnr = I
6
R 215 000 X ──── X n = R 6 450
100
12 900 X n = 6 450
6 450
r = ────
12 900
= 0,5 jaar / years
= 6 maande / months
dd = 4 maande / months
[ 1. ]
1.15
A = R 3 068, P = R 2 600, n = 2 jaar / years
I = A ─ P
= R 3 068 ─ R 2 600
= R 468
hh = R 468
[ 1. ]
Pnr = I
r
R 2 600 X ──── X 2 = R 468
100
52 X r = 468
468
r = ────
52
= 9 %
gg = 9 %
[ 1. ]
1.2
P = R 110 600, r = 12 % , n = 3 jaar / years
I = Pnr
12
= R 110 600 X ──── X 3
100
= R 39 816
c = R 39 816
[ 1. ]
A = P + I
= R 110 600 + R 39 816
= R 150 416
d = R 150 416
[ 1. ]
1.4
P = R 14 800, r = 6 % , n = 7 jaar / years
I = Pnr
6
= R 14 800 X ──── X 7
100
= R 6 216
g = R 6 216
[ 1. ]
A = P + I
= R 14 800 + R 6 216
= R 21 016
h = R 21 016
[ 1. ]
1.6
P = R 21 400, r = 9 % , n = 3 jaar / years
I = Pnr
9
= R 21 400 X ──── X 3
100
= R 5 778
n = R 5 778
[ 1. ]
A = P + I
= R 21 400 + R 5 778
= R 27 178
p = R 27 178
[ 1. ]
1.8
A = R 186 470, r = 18 %, P = R 128 600
I = A ─ P
= R 186 470 ─ R 128 600
= R 57 870
s = R 57 870
[ 1. ]
Pnr = I
18
R 128 600 X ──── X n = R 57 870
100
23 148 X n = 57 870
57 870
n = ────
23 148
= 2,5
t = 2,5
[ 1. ]
1.10
A = R 49 974,50, P = R 39 350, n = 3 jaar / years
I = A ─ P
= R 49 974,50 ─ R 39 350
= R 10 624,50
w = R 10 624,50
[ 1. ]
Pnr = I
r
R 39 350 X ──── X 3 = R 10 624,50
100
1180,5 X r = 10 624,50
10 624,50
r = ────
1180,5
= 9
x = 9 %
[ 1. ]
1.12
A = R 5 544, I = R 144, r = 8 %
P = A ─ I
= R 5 544 ─ R 144
= R 5 400
aa = R 5 400
[ 1. ]
Pnr = I
8
R 5 400 X ──── X n = R 10 624,50
100
432 X n = 144
144
r = ────
432
= 0,3333 jaar / years
= 4 maande / months
bb = 4 maande / months
[ 1. ]
1.14
A = R 2 312 500, I = R 462 500,
n = 30 maande / months
P = A ─ I
= R 2 312 500 ─ R 462 500
= R 1 850 000
ee = R 1 850 000
[ 1. ]
Pnr = I
r 30
R 1 850 000 X ─── X ─── = R 462 500
100 12
46 250 X r = 462 500
462 500
r = ────
46 250
= 10 %
ff = 10 %
[ 1. ]
1.16
A = R 101 385,60, P = R 85 920,
n = 18 maande / months
I = A ─ P
= R 101 385,60 ─ R 85 920
= R 15 465,60
mm = R 15 465,60
[ 1. ]
Pnr = I
r 18
R 85 920 X ─── X ─── = R 15 465,60
100 12
1288,8 X r = 462 500
15 465,60
r = ───────
1288,8
= 12 %
kk = 12 %
[ 1. ]
Antwoorde / Answers 2
2.1
P = R 13 250, r = 4 % , n = 3 jaar / years
A = P(1 + i)
n
4
= R 13 250 X (1 + ────)
3
100
= R 14 904,45
a = R 14 904,45
[ 2. ]
I = A ─ P
= R 14 904,45 ─ R 13 250
= R 1 654,45
b = R 1 654,45
[ 2. ]
2.3
P = R 116 000, r = 12,5 % , n = 6 jaar / years
A = P(1 + i)
n
12,5
= R 116 000 X (1 + ────)
6
100
= R 235 165,24
e = R 235 165,24
[ 2. ]
I = A ─ P
= R 235 165,24 ─ R 116 000
= R 119 165,24
f = R 119 165,24
[ 2. ]
2.5
P = R 60 000, r = 8,5 % , n = 4,5 jaar / years
maandeliks saamgestel / compounded monthly
n = 4,5 X 12 periodes / periods
A = P(1 + i)
n
8,5
= R 60 000 X (1 + ────────)
4,5 X 12
100 X 12
= R 87 838,18
k = R 87 838,18
[ 2. ]
I = A ─ P
= R 87 838,18 ─ R 60 00000
= R 27 838,18
m = R 27 838,18
[ 2. ]
2.7
P = R 82 000, r = 20 % , n = 3 jaar / years
kwartaalliks saamgestel / compounded quarterly
n = 3 X 4 periodes / periods
A = P(1 + i)
n
20
= R 82 000 X (1 + ────────)
3 X 4
100 X 4
= R 147 260,22
q = R 147 260,22
[ 2. ]
I = A ─ P
= R 147 260,22 ─ R 82 000,00
= R 65 260,22
r = R 65 260,22
[ 2. ]
2.9
P = R 180 000, r = 18 % , n = 3,5 jaar / years
maandeliks saamgestel / compounded monthly
n = 3,5 X 12 periodes / periods
A = P(1 + i)
n
18
= R 180 000 X (1 + ────────)
3,5 X 12
100 X 12
= R 336 392,48
u = R 336 392,48
[ 2. ]
I = A ─ P
= R 336 392,48 ─ R 180 000,00
= R 156 392,48
v = R 156 392,48
[ 2. ]
2.2
P = R 65 000, r = 8 % , n = 4 jaar / years
A = P(1 + i)
n
8
= R 65 000 X (1 + ────)
4
100
= R 88 431,78
c = R 88 431,78
[ 2. ]
I = A ─ P
= R 88 431,78 ─ R 65 000
= R 23 421,78
d = R 23 421,78
[ 2. ]
2.4
P = R 128 000, r = 22 % ,
n = 2 jaar / years
kwartaalliks saamgestel / compounded quarterly
n = 2 X 4 periodes / periods
A = P(1 + i)
n
22
= R 128 000 X (1 + ──────)
2 X 4
100 X 4
= R 196 439,87
g = R 196 439,87
[ 2. ]
I = A ─ P
= R 196 439,87 ─ R 128 000
= R 68 439,87
h = R 68 439,87
[ 2. ]
2.6
P = R 28 400 000, r = 7,5 % ,
n = 2,5 jaar / years
halfjaalliks saamgestel / compounded semi-annually
n = 2,5 X 2 periodes / periods
A = P(1 + i)
n
7,5
= R 28 400 000 X (1 + ──────)
2,5 X 2
100 X 2
= R 34 139 634,48
n = R 34 139 634,48
[ 2. ]
I = A ─ P
= R 34 139 634,48 ─ R 28 400 000,00
= R 5 739 634,48
p = R 5 739 634,48
[ 2. ]
2.8
P = R 1 537 000, r = 15 % ,
n = 1,5 jaar / years
maandeliks saamgestel / compounded monthly
n = 1,5 X 12 periodes / periods
A = P(1 + i)
n
15
= R 1 537 000 X (1 + ───────)
1,5 X 12
100 X 12
= R 1 922 137,46
s = R 1 922 137,46
[ 2. ]
I = A ─ P
= R 1 922 137,46 ─ R 1 537 000,00
= R 385 137,54
t = R 385 137,54
[ 2. ]
2.10
P = R 2 500 600, r = 8 % ,
n = 4 jaar / years
halfjaarliks saamgestel / compounded semi-annually
n = 4 X 2 periodes / periods
A = P(1 + i)
n
8
= R 2 500 600 X (1 + ───────)
4 X 2
100 X 2
= R 3 422 243,77
w = R 3 422 243,77
[ 2. ]
I = A ─ P
= R 3 422 243,77 ─ R 2 500 600,00
= R 921 643,77
x = R 921 643,77
[ 2. ]
Opsie / Option 1
P = R 18 000, r = 8,5 % , n = 18 maande / months
A = P(1 + i)n
8,5
= R 18 000 X (1 + ────────)18
100 X 12
= R 20 438,54
Opsie / Option 2
P = R 18 000, r = 10 % , n = 30 maande / months
30 maande / months = 2,5 jaar / years
= 2,5 X 4
= 10 periodes / periods
A = P(1 + i)n
10
= R 18 000 X (1 + ────────)2,5 × 4
100 X 4
= R 23 041,52
Opsie 1 is die goedkoopste en dus die beste. / Option 1 is the cheaper and thus better option.
[ 3. ]