4
{–1000}→[PV]
{5×4}→[N]
{14/4}→[I/Y]
{0}→[PMT]
[CPT]→[FV] = $1,989.79
3. Ordinary Annuities
In an ordinary annuity, a constant cash flow is either paid or received at the end of a
particular payment period over the life of an investment or liability. Here, we begin
use of the [PMT] key.
Example: You would like to buy a 9%, semi-annual, 8-year corporate bond with a
par value of $1,000 (par value represents the terminal value of the bond). Compute
the value of this bond today if the appropriate discount rate is 8%. Here, the 9% is
the coupon rate of the bond and represents the annual cash flow associated with the
bond. Hence, the annual PMT = (0.09) × ($1,000) = $90.
The value of the bond today is:
{8 × 2}→[N]
{$90/2}→[PMT]
{8/2}→[I/Y]
{$1,000}→[FV]
[CPT]→[PV] = -$1,058.26
Example: You will receive $100 per month for the next three years and you have
nothing today. The appropriate annual interest rate is 12%. Compute your
accumulated funds at the end of three years.
{3×12}→[N]
{0}→[PV]
{100}→[PMT]
{12/12}→[I/Y]
[CPT]→[FV] = -$4,307.69
4. Annuity Due
In an annuity due, you receive each constant annuity cash flow at the beginning of
each period. You must set your calculator to BGN mode by pressing
[2nd]→[BGN]→[2nd]→[SET]. BGN will appear in the calculator’s LCD screen.
HOW TO USE YOUR TI BA II PLUS CALCULATOR
©2003 Schweser Study Program
5
Example: You will receive $100 per month for the next three years and you have
nothing today. The appropriate annual interest rate is 12%. Compute your
accumulated funds at the end of three years:
{3×12}→[N]
{0}→[PV]
{100}→[PMT]
{12/12}→[I/Y]
[CPT]→[FV] = -$4,350.76
Notice that the future value is larger in this case because you receive each cash flow
at the beginning of the period, so each cash flow is exposed to one additional
compounding period.
5. Continuous Compounding and Discounting
If the number of compounding periods is said to be continuous, what this means is
that the time between compounding periods is infinitesimally small. To discount and
compound, you need the magic number e = 2.718281.
The formula for continuous compounding of a single cash flow is:
FV = PV × (ert)
The formula for continuous discounting is:
PV = FV × (e-rt)
where:
r = the annualized interest rate
t = the number of years
Example: You have $100 today and have been offered a 6-month continuously
compounded investment return of 10%. How much will the investment be worth?
Step 1: Compute r × t =
0.1 × 0.5 = 0.05
Note that you always use the decimal representative of both the interest
rate and time when performing these computations
Step 2: Compute er×t
{0.05}→[2nd]→[ex] = 1.05127
HOW TO USE YOUR TI BA II PLUS CALCULATOR
©2003 Schweser Study Program
6
Step 3: Find the future value
$100×1.05127 = $105.13
Example: You will receive $1,000 eighteen months from today and would like to
compute the present value of this amount at 8% with continuous compounding.
Step 1: Compute –r × t
–0.08×1.5 = –0.12
Step 2: Compute e–rt
{–0.12}→[2nd]→[ex] = 0.88692
Step 3: Find the present value
$1,000×0.88692 = 886.92
6. Internal Rate of Return (IRR) and Net Present Value (NPV)
Just in case there is a question on the examination that asks for an IRR calculation,
the keystrokes are as indicated in the following example.
To use the IRR and NPV functions in your TI-BA II Plus, you must first familiarize
yourself with the up and down arrows (↑↓) at the top of the keyboard. These keys
will help you navigate your way through the data entry process. After entering the
initial cash flow, you will need to key [↓] once. After each subsequent cash flow,
(until the final cash flow) you will need to key [↓] twice, once to enter the cash flow
and once to scroll through the display that shows the frequency of the cash flow.
After entering the final cash flow, key [↓] once only.
Example: Project X has the following expected after-tax net cash flows. The firm’s
cost of capital is 10%.
Expected Net After-Tax Cash Flows – Project X
Year Cash Flow
0 (initial outlay) -$2,000
1 1,000
2 800
3 600
4 200
{–1000}→[PV]
{5×4}→[N]
{14/4}→[I/Y]
{0}→[PMT]
[CPT]→[FV] = $1,989.79
3. Ordinary Annuities
In an ordinary annuity, a constant cash flow is either paid or received at the end of a
particular payment period over the life of an investment or liability. Here, we begin
use of the [PMT] key.
Example: You would like to buy a 9%, semi-annual, 8-year corporate bond with a
par value of $1,000 (par value represents the terminal value of the bond). Compute
the value of this bond today if the appropriate discount rate is 8%. Here, the 9% is
the coupon rate of the bond and represents the annual cash flow associated with the
bond. Hence, the annual PMT = (0.09) × ($1,000) = $90.
The value of the bond today is:
{8 × 2}→[N]
{$90/2}→[PMT]
{8/2}→[I/Y]
{$1,000}→[FV]
[CPT]→[PV] = -$1,058.26
Example: You will receive $100 per month for the next three years and you have
nothing today. The appropriate annual interest rate is 12%. Compute your
accumulated funds at the end of three years.
{3×12}→[N]
{0}→[PV]
{100}→[PMT]
{12/12}→[I/Y]
[CPT]→[FV] = -$4,307.69
4. Annuity Due
In an annuity due, you receive each constant annuity cash flow at the beginning of
each period. You must set your calculator to BGN mode by pressing
[2nd]→[BGN]→[2nd]→[SET]. BGN will appear in the calculator’s LCD screen.
HOW TO USE YOUR TI BA II PLUS CALCULATOR
©2003 Schweser Study Program
5
Example: You will receive $100 per month for the next three years and you have
nothing today. The appropriate annual interest rate is 12%. Compute your
accumulated funds at the end of three years:
{3×12}→[N]
{0}→[PV]
{100}→[PMT]
{12/12}→[I/Y]
[CPT]→[FV] = -$4,350.76
Notice that the future value is larger in this case because you receive each cash flow
at the beginning of the period, so each cash flow is exposed to one additional
compounding period.
5. Continuous Compounding and Discounting
If the number of compounding periods is said to be continuous, what this means is
that the time between compounding periods is infinitesimally small. To discount and
compound, you need the magic number e = 2.718281.
The formula for continuous compounding of a single cash flow is:
FV = PV × (ert)
The formula for continuous discounting is:
PV = FV × (e-rt)
where:
r = the annualized interest rate
t = the number of years
Example: You have $100 today and have been offered a 6-month continuously
compounded investment return of 10%. How much will the investment be worth?
Step 1: Compute r × t =
0.1 × 0.5 = 0.05
Note that you always use the decimal representative of both the interest
rate and time when performing these computations
Step 2: Compute er×t
{0.05}→[2nd]→[ex] = 1.05127
HOW TO USE YOUR TI BA II PLUS CALCULATOR
©2003 Schweser Study Program
6
Step 3: Find the future value
$100×1.05127 = $105.13
Example: You will receive $1,000 eighteen months from today and would like to
compute the present value of this amount at 8% with continuous compounding.
Step 1: Compute –r × t
–0.08×1.5 = –0.12
Step 2: Compute e–rt
{–0.12}→[2nd]→[ex] = 0.88692
Step 3: Find the present value
$1,000×0.88692 = 886.92
6. Internal Rate of Return (IRR) and Net Present Value (NPV)
Just in case there is a question on the examination that asks for an IRR calculation,
the keystrokes are as indicated in the following example.
To use the IRR and NPV functions in your TI-BA II Plus, you must first familiarize
yourself with the up and down arrows (↑↓) at the top of the keyboard. These keys
will help you navigate your way through the data entry process. After entering the
initial cash flow, you will need to key [↓] once. After each subsequent cash flow,
(until the final cash flow) you will need to key [↓] twice, once to enter the cash flow
and once to scroll through the display that shows the frequency of the cash flow.
After entering the final cash flow, key [↓] once only.
Example: Project X has the following expected after-tax net cash flows. The firm’s
cost of capital is 10%.
Expected Net After-Tax Cash Flows – Project X
Year Cash Flow
0 (initial outlay) -$2,000
1 1,000
2 800
3 600
4 200
