577

P1: FXS/ABE
P2: FXS
9780521740517c21.xml
CUAU031-EVANS
August 25, 2010
19:29
Chapter 21 – Applications of financial mathematics
577
How to determine flat rate depreciation and book value using the TI-Nspire CAS
A computer system costs $9500 to buy and decreases in value by 10% of the purchase
price each year.
a What is the amount of depreciation after 4 years?
b Find its book value after 4 years.
Steps
1 Write expressions for depreciation
9500 × 10 × t
and book value.
depreciation =
100
9500 × 10 × t
Pr t
= 9500 −
book value = P −
100
100
2 Start a new document by pressing
+ , and select
Add Lists & Spreadsheet.
a Name three lists: year (for t),
depreciation, and book value,
respectively.
Hint: Use
+
for the underscore
or just type bookvalue.
b Enter the numbers 1, 2, 3, . . . , 10
into the list year.
c Move the cursor to the grey
formula cell of the list depreciation
and type
= (9500 × 10 × year )/100
to calculate the values
Press
for depreciation.
3 Move the cursor to the grey formula cell
of the list book value and type
= 9500 − (9500 × 10 × year )/100
to calculate the values for book
Press
value.
Notes:
1
An alternative formula to use to calculate
the list book value would be
= 9500 − depreciation
2
You can use the
key to display the
variable list rather than retyping the list
names.
4 Scrolling through the table we see that
after 4 years the depreciation is $3800 and
the book value is $5700.
Cambridge University Press
(c) Jones, Evans & Lipson 2010
Photocopying is restricted under law and this material must not be transferred to another party
P1: FXS/ABE
P2: FXS
9780521740517c21.xml
CUAU031-EVANS
580
August 25, 2010
19:29
Essential Further Mathematics — Module 4 Business-related mathematics
How to determine reducing balance depreciation and book value using the TI-Nspire CAS
A computer system costs $9500 to buy and decreases in value by 20% each year.
a What is the book value of the computer after 4 years?
b By how much has the value of the computer depreciated over the 4 years?
Steps
1 Write expressions for book value
and depreciation.
20 t
book value = 9500 × 1 −
100
20 t
depreciation = 9500 − 9500 × 1 −
100
2 Start a new document by pressing
+ , and select Add Lists &
Spreadsheet.
a Name three lists, year (t),
book value and depreciation,
respectively.
Hint: Use
+
for the underscore
or just write as bookvalue.
b Enter the numbers 1, 2, 3, . . . , 10
into the list year.
c Move the cursor to the grey
formula cell of the list
book value and type
= (9500 × (1 − 20/100)∧ year
to calculate the values
Press
for book value.
3 Move the cursor to the grey formula cell
of the list depreciation and type
= 9500 − (9500 × (1 − 20/100)∧ year
to calculate the values for
Press
depreciation.
Note: You can use the
key to display
the variable list rather than retyping in the
list names.
4 Scrolling through the table, we see that
after 4 years the book value is $3891.20
and the depreciation is $5608.80.
Cambridge University Press
(c) Jones, Evans & Lipson 2010
Photocopying is restricted under law and this material must not be transferred to another party
P1: FXS/ABE
P2: FXS
9780521740517c21.xml
CUAU031-EVANS
August 25, 2010
19:29
Chapter 21 – Applications of financial mathematics
585
How to use Finance Solver on the TI-Nspire CAS
Steps
then c (or
on the
1 Press
Touchpad) then to open the
Scratchpad: Calculate.
2 Press b >Finance>Finance Solver.
3 To use Finance Solver you need to know
the meaning of each of its symbols. These
are as follows:
• N is the total number of payments
• I(%) is the annual interest rate
• PV is the present value of the loan or
investment
• Pmt is the amount paid at each payment
• FV is the future value of the loan or
investment
• PpY is the number of payments per year
• CpY is the number of times the interest is
compounded per year. (It is almost always
the same as PpY.)
• PmtAt is used to indicate whether
the interest is compounded at the end
or at the beginning of the time period.
Leave this set at END.
Note: Use
to move between boxes and use to make a selection within a box.
Press
to move down to the next entry box. Press
+
(
+
on the Touchpad)
to move up.
4 When using Finance Solver to solve loan and investment problems, there will be one
to
unknown quantity. To find its value, move the cursor to its entry box and press
solve.
Now we can consider each of the applications of the finance solver separately.
Cambridge University Press
(c) Jones, Evans & Lipson 2010
Photocopying is restricted under law and this material must not be transferred to another party