#### Interest, compound growth, appreciation, depreciation, inflation

1. Use the formulae for simple interest and then calculate the value of each letter in the table:

 P r% t (years) A I
1.1
 1 200 5 2 a b
1.2
 22 500 7 4 c d
1.3
 23 650 9 3,5 e f
1.4
 80 000 12 8 g h
1.5
 m 18 1,5 149 860 n
1.6
 p 25 0,5 737 820 q
1.7
 r 4 4 2 668 s
1.8
 t 5,2 3 18 496 v
1.9
 28 650 w 5,5 50 710,50 x
1.10
 108 000 y 8 182 304 z
1.11
 530 000 aa 15 1 484 000 bb
1.12
 850 800 cc 13 2 012 142 dd
1.13
 850 11,4 ee 1 189,15 ff
1.14
 6 820 8,8 gg 8 170,36 hh
1.15
 9 730 6,4 mm nn 3 736,32
1.16
 12 500 5,8 pp qq 6 343,75

2. Use the formula for compound interest and then calculate the value of each letter in the table:

 P r% When Time Number A compounded (years) of periods
2.1
 250 6 annually 1 a b
2.2
 1 200 10 semi-annually 1 c d
2.3
 13 450 8 quarterly 5 e f
2.4
 21 560 9,4 monthly g 18 h
2.5
 124 500 12 monthly m 36 n
2.6
 p 8,8 quarterly q 16 261 201,25
2.7
 r 9,5 semi-annually 5,5 s 201 594,98
2.8
 t 11,5 annually 2,5 u 216 769,99
2.9
 v 8,4 semi-annually w 5 10 465,94
2.10
 6 400 x quarterly 8 y 9 829,70
2.11
 240 000 aa quarterly 3 bb 306 173,32
2.12
 450 600 cc quarterly 2,5 dd 608 514,80
2.13
 180 750 ee semi-annually ff 6 226 080,15
3.
R6 700 is invested and 4 years later the balance in the account is R10 380,27.
Interest is compounded semi-annually. Calculate the annual rate of interest,
correct to two decimal digits.
4.
A certain piece of machinery now costs R116 850. What will the machine cost
in 5 years time if the rate of inflation is 7,4% p.a.?
5.
The price of a DVD player is R1 245. What will the player cost 3 years later
if the rate of inflation is 5,2% p.a.?
6.
At present a colony of penguins consists of 650 birds. If the rate of increase
is 2,1%, how many birds will there be in 3 years time?
7.
The value of a motor car is R120 000. What will its value be in 5 years time if
the rate of depreciation is 15% p.a. and straight line depreciation is used?
8.
Straight line depreciation is used to determine the value of a tractor 4 years
from now if the rate of depreciation is 12% p.a. and the present value of
the tractor is R450 000.
9.
A machine has a value of R84 500. What will the value of the machine be 3 years
from now if value is decreased at 18% p.a. using the reducing-balance method?
10.
A business buys a machine that costs R215 700. The value of the machine
depreciates at 11,2% p.a. using the diminishing-balance method.
Determine the value of the machine at the end of 5 years.
11.
A business buys a lorry that costs R530 650. The value of the lorry depreciates
at 8% p.a. using the diminishing-balance method.
11.1
Determine the value of the lorry at the end of 5 years.
11.2
Determine the value of a new lorry at the end of 5 years if the rate of inflation
is 7% p.a.
11.3
Determine the amount that the business must now invest to buy a new lorry at
the end of the 5 years if the rate of interest remains constant at 7,2% p.a.
compounded quarterly?
12.
The value of a machine is diminished at 12% per annum according to the
diminishing-balance method. After how many years will the value of the machine
be a quarter of its original cost price?
13.
The value of a machine depreciates at 12% per annum according to the
diminishing-balance method. After how many years will the value of the machine
be diminished by a third of its original cost price?
14.
Jasper invests R40 000 for 5 years. During the first two years the interest rate is
18% p.a. compounded monthly. The rate of interest is now increased to 12% p.a.
compounded quarterly. Calculate the value of the investment at the
end of 5 years.
15.
James invests a certain amount for 3 years. During the first year the rate of
interest is 8% per annum, quarterly compounded and for the last two years the
rate is 10% per year, compounded semi-annually. At the end of the 3 years the
value of the investment is R23 682,66. Determine the amount originally invested.
16.
John invests R30 000 for 5 years. The interest rate is 18% p.a., compounded
monthly. After 2 years he withdraws R8 000 and 1 year later he withdraws a
further R6 000. What is the value of the investment at the end of the 5 years?
17.
Mary invests R130 000 for 2 years at an interest rate of 6% per annum,
compounded monthly. After 4 months she withdraws R20 000 and 7 months later
another amount of R15 000. What is the value of the investment at the end of
the 2 year period?
18.
An amount of R82 000 is invested for 3 years at a constant rate of interest
of 8% p.a. compounded semi-annually. After 6 months a further R8 000 is
invested and 1 year later another R12 000 is invested. Determine the value of
the investmen at the end of the 3 year period.
19.
John invests R65 000 for 2 years at an interest rate of 8% compounded quarterly.
After 4 months he invests a further R5 000. One year later he withdraws R12 000.
How much money is there in the account at the end of the 2 year period?
20.
William invests R55 600 at a rate of interest of 15% p.a., monthly compounded
for 5 years. After 1 year he invests a further R12 000. One year later he
witdraws R20 000 and the rate of interest is decreased to 10% p.a., quarterly
compounded. Four years after the initial investment William invests a further
R8 300. What is the value of the investment after 5 years?
21.
R20 000 is invested at 6% p.a., monthly compounded. Calculate the effective
interest rate.
22.
The effective interest rate is 2,02%. What is the nominal rate of interest if it
is compounded quarterly?
23.
R35 500 is invested for 3 years at 8% p.a., semi-annually compounded.
23.1
Calculate the value of the investment after 3 years.
23.2
Calculate the effective interest rate.