Grade 11  More Exercises.
Interest, compound growth, appreciation, depreciation, inflation
1. 
Use the formulae for simple interest and then calculate
the value of each letter in the table: 




1.1 

1.2 

1.3 

1.4 

1.5 

1.6 

1.7 

1.8 

1.9 

1.10 

1.11 
530 000 
aa 
15 
1 484 000 
bb 

1.12 
850 800 
cc 
13 
2 012 142 
dd 

1.13 

1.14 

1.15 

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 

2.2 
1 200 
10 
semiannually 
1 
c 
d 

2.3 

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 
semiannually 
5,5 
s 
201 594,98 

2.8 
t 
11,5 
annually 
2,5 
u 
216 769,99 

2.9 
v 
8,4 
semiannually 
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 
semiannually 
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 semiannually. 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 reducingbalance method?
10.
A business buys a machine that costs R215 700. The value of the machine
depreciates at 11,2% p.a. using the diminishingbalance 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 diminishingbalance 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
diminishingbalance 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
diminishingbalance 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 semiannually. 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 semiannually. 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., semiannually compounded.
23.1
Calculate the value of the investment after 3 years.
23.2
Calculate the effective interest rate.