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 |
semi-annually |
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 |
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.