#### Interest - simple and compound.

1.1
a = 5 503,75 ; b = 36 953,75
1.2
c = 39 816 ; d = 150 416
1.3
e = 137,5 ; f = 1 387,50
1.4
g = 6 ; h = 6 216
1.5
j = 25,2 ; k = 15 750
1.6
m = 9 ; n = 5 778
1.7
p = 1 250 000 ; q = 1 531 250
1.8
r = 1 050 ; s = 1 302
1.9
t = 2 500 ; u = 3 550
1.10
v = 5 ; w = 7 706,25
1.11
x = 2 ; y = 14 697
1.12
z = 9 ; aa = 224 358,80
1.13
ab = 12 500 ; ac = 16 250
2.
Calculate the interest for the first period by using the formula for simple interest.
Add this interest to the capital. This amount is the capital for the second period.
Calculate the interest for the second period and repeat as above. Do this for each of the remaining periods.
Capital for 1st period = P1 ; interest rate = r% p.a.; how often is interest compounded m times per year and the investment is for t years.
Calculate the number of periods, n, and the interest rate for the period i :
r (interest rate p.a.)
Number of periods = n = m x t    i (interst rate / period) = ——————————————
100   x   m (number of periods per year)
2.1
P = R13 250;   r = 4%; t = 4 years
2.2
P = R65 000;   r = 8%; t = 1 year
and the interest is compounded yearly.
and the interest is compounded quarterly.
number of periods per year = 1
number of periods per year = 4
total number of periods = 1 x 4 = 4
total number of periods = 4 x 1 = 4
4
8
i   =  ——————   =   0,04
i   =  ——————   =   0,02
100   x   1
100   x   4
Interest for 1st period = Pi = R13 250 x 0,04
Interest for 1st period = Pi = R65 000 x 0,02
= R530,00
= R1 300,00
Capital for 2nd period = P + I
Capital for 2nd period = P + I
P2 = R13 250,00 + 530,00
P2 = R65 000 + 1 300
= R13 780,00
= R66 300
Interest for 2nd period = R13 780 x 0,04
Interest for 2nd period = R66 300 x 0,02
I2 = R551,20
I2 = R1 326,00
P3 = P2 + I2 = R14 331,20
P3 = P2 + I2 = R67 626,00
I3 = P2 x i = R573,248 = R573,25
P3 = P2 x i = R1 352,52
P4 = P3 + I3 = R14 904,45
P4 = P2 + I2 = R68 978,52
I4 = P3 x i = R596,18
P4 = P3 x i = R1 379,57
Amount payable = A = R15 500,63
Amount payable = A = R70 358,09
a = R15 500,63     and   b = R2 250,63
c = R70 358,09     and   d = R5 358,09
2.3   e = R119 165,24     and   f = R235 165,24
2.4   g = R11 535,46     and   h = R24 335,46
2.5   k = R27 838,18     m = R87 838,18
2.6   n = R5 739 634,48     p = R34 139 634,50
2.7   q = R65 260,22     r = R147 260,22
2.8   s = R385 137,45     t = R1 922 137,45
2.9   u = R156 392,48     v = R336 392,48
2.10   w = R921 643,77     x = R3 422 243,77
3.
Option 1:
Option 2:
P = R18 000,00;   r = 8,5%; t = 1,5 years
P = R18 000,00;   r = 10%;t = 2,5 years
and the interest is compounded monthly.
and the interest is compounded quarterly.
number of periods per year = 2
number of periods per year = 4
total periodes = 12 x 1,5 = 18
total periodes = 4 x 2,5 = 10
8,5
10
i   =  ——————   =   0,00708333
i   =  ——————   =   0,025
100   x   12
100   x   4
A1 = P1 x (1 + i)
A1 = P1 x (1 + i)
= R18 000,00 x 1,00708333
= R18 000,00 x 1,025
= R18 127,50
= R18 450,00
A2 = R18 127,50 x 1,00708333
A2 = R18 450,00 x 1,025
= R18 255,90
= R18 911,25
A3 = R18 255,90 x 1,00708333
A3 = R18 911,25 x 1,025
= R18 385,21
= R19 384,03
Repeat 15 times.
Repeat 7 times.
Finale amount = A18 = R20 438,54
Finale amount = A10 = R23 041,52
Option 1 is the cheaper because the final amount payable, is smaller.
4.1
R100 is invested.
4.2
At 6% the amount is R106, i.e. R106 - R100 = R6 interest is earned and
at 12% the amount is R112, i.e. R12 interest is earned.
4.3
Thus it appears as if the interest at 12% is double the interest at 6% . At 36 months the
interest earned at 12% is more than double the interest earned at 6%. The interest at 12%
is therefore not double the interest at 6%.
4.4
At 10 months the investment is valued at more than R110.
P = R100 ; i = 0,01 Thus I1 = R100 x 0,01 = R1 and A1 = R100 + 1 = R101

 Month P (R) I (R) A (R) Month P (R) I (R) A (R) 1 100,00 1,00 101,00 6 105,10 1,05 106,15 2 101,00 1,01 102,01 7 106,15 1,06 107,21 3 102,01 1,02 103,03 8 107,21 1,07 108,28 4 103,0 1,03 104,06 9 108,28 1,08 109,36 5 104,06 1,04 105,10 10 109,36 1,09 110,45