Chapter 6
Time Value of Money
Concepts
Copyright © 2015 McGraw-Hill Education. All rights reserved.
Time Value of Money
• Means money can be invested today to earn
interest and grow to a larger dollar amount in the
future
Example:
Invested in
bank
$100
Annual
yield
6%
Future
value
$106
• Useful in valuing a variety of assets and liabilities
LO6-1
Simple versus Compound Interest
Interest
• Amount of money paid or received in excess of the
amount of money borrowed or lent
Simple Interest
Initial
Interest
Period
×
×
investment
rate
of time
Compound Interest
• Includes interest not only on the initial investment
but also on the accumulated interest in previous
periods
LO6-1
Simple Interest
Example:
What is the simple interest earned each year on a $1,000
investment paying 10% interest?
Investment × Interest rate × Time period = Simple interest
1 Year
=
$100
×
$1,000 ×
10%
LO6-1
Compound Interest
Example:
Cindy Johnson invested $1,000 in a savings account paying 10%
interest compounded annually. How much interest will she
earn in each of the next three years, and what will be her
investment balance after three years?
Date
Interest
Balance
(Interest rate ×
Outstanding Balance)
Initial deposit
End of year 1
End of year 2
End of year 3
10% × $1,000 = $100
10% × $1,100 = $110
10% × $1,210 = $121
$1,000
$1,100
$1,210
$1,331
LO6-1
Compound Interest
Effective rate
• Actual rate at which money grows per year
Example:
Assuming an annual rate of 12%:
Compounded
Semiannually
Quarterly
Monthly
Interest Rate Per
Compounding Period
12% ÷ 2 = 6%
12% ÷ 4 = 3%
12% ÷ 12 = 1%
LO6-1
Compound Interest
Example:
Cindy Johnson invested $1,000 in a savings account paying
10% interest compounded twice a year. What will be her
investment balance at the end of the year? What is the
effective annual interest rate?
Interest
10% ÷ 2 = 5%
(Interest rate ×
Date
Outstanding balance)
Balance
Initial deposit
$1,000.00
After six months
5% × $1,000 = $50.00
$1,050 .00
End of year 1
5% × $1,050 = $52.50
$1,102.50
$1,102.50 – $1,000
Effective annual interest rate = $102.50 ÷ $1,000 = 10.25%
LO6-2
Valuing a Single Cash Flow Amount
Future Value of a Single Amount
• The amount of money that a dollar will grow to at
some point in the future
FV = I (1 + i)ⁿ
I = Amount invested at the beginning of the period
i = Interest rate
n = Number of compounding periods
LO6-2
Future Value of a Single Amount
Example:
Cindy Johnson invested $1,000 in a savings account for
three years paying 10% interest compounded annually.
$1,000
0
FV = I × FV Factor
FV = $1,000 × 1.331
FV = $1,331
End of
year 1
End of
year 2
Future
value
$1,331
End of
year 3
LO6-3
Present Value of a Single Amount
• Today’s equivalent to a particular amount in the
future
FV
n
FV = PV (1 + i)
PV
= (1 + i) n
Example:
$1,331
$1,331
PV
=
= $1,000
= (1 + .10)3
1.331
LO6-3
Present Value of a Single Amount
Example:
The present value of $1,331 received at the end of
three years:
PV = FV × PV Factor
PV = $1,331 × .75131
PV = $1,000
LO6-3
Relation between the Present Value and the
Future Value
End of
year 1
0
$100
End of
year 2
$110
End of
year 3
$121
$1,000
PV
• Future value entails the addition of interest
• Present value entails the removal of interest
• Accountants use PV calculations much more
frequently than FV
$1,331
FV
Concept Check √
The Versa Tile Company purchased a delivery truck on February 1, 2016.
The agreement required Versa Tile to pay the purchase price of $44,000 on
February 1, 2017. Assuming an 8% rate of interest, to calculate the price of
the truck Versa Tile would multiply $44,000 by the:
a.
Future value of an ordinary annuity of $1.
b.
Present value of $1.
c.
Present value of an ordinary annuity of $1.
d.
Future value of $1.
The calculation is for the present value today of the $44,000 to be
received one year from now.
LO6-4
Solving for Other Values When FV and PV Are
Known
Determining an Unknown Interest Rate
Suppose a friend asks to borrow $500 today and promises
to repay you $605 two years from now. What is the
annual interest rate you would be agreeing to?
Present
value
$500
0
Future
value
$605
End of
year 1
n = 2, i = ?
End of
year 2
LO6-4
Determining an Unknown Interest Rate
(continued)
$500 (present value) = $605 (future value) × PVF*
*Present value of $1; n = 2, i = ?
$500 (present value) ÷ $605 (future value) = 0.82645*
*Present value of $1; n = 2, i = ?
i = 10%
.
.75131
.751
31
LO6-4
Solving for Other Values When FV and PV Are
Known
Determining an Unknown Number of Periods
You want to invest $10,000 today to accumulate $16,000 for
graduate school. If you can invest at an interest rate of 10%
compounded annually, how many years will it take to
accumulate the required amount?
Present
value
Future
value
$10,000
$16,000
0
End of
year 1
End of
year 2
n = ?, i = 10%
End of
year n-1
End of
year n
LO6-4
Determining an Unknown Number of Periods
(continued)
$10,000 (present value) = $16,000 (future value) × PVF*
*Present value of $1; i = 10%, n = ?
$10,000 (present value) ÷ $16,000 (future value) = 0.625*
*Present value of $1; i = 10%, n = ?
n=5
.75131
.751
31
.
.
LO6-4
Preview of Accounting Applications of Present
Value Techniques — Single Cash Amount
Most monetary assets and monetary liabilities are
valued at the present value of future cash flows
Monetary assets
• Include money and claims to receive money in the
future, the amount of which is fixed or determinable
Examples:
Cash and most receivables
Monetary liabilities
• Obligations to pay amounts of cash in the future, the
amount of which is fixed or determinable
Example:
Notes payable
LO6-4
Valuing a Note: One Payment, Explicit Interest
Example:
The Stridewell Wholesale Shoe Company manufactures
athletic shoes for sale to retailers. The company recently
sold a large order of shoes to Harmon Sporting Goods for
$50,000. Stridewell agreed to accept a note in payment
for the shoes requiring payment of $50,000 after one year
plus interest at 10%.
Present
value
Future
value
$55,000
End of
year 1
?
0
n = 1, i = 10%
LO6-4
Valuing a Note: One Payment, Explicit Interest
$55,000 (future value) × 0.90909* = $50,000 (present value)
*Present value of $1; n = 1, i = 10%
LO6-4
Valuing a Note: One Payment, No Interest Stated
Example:
The Stridewell Wholesale Shoe Company recently sold a
large order of shoes to Harmon Sporting Goods. Terms of
the sale require Harmon to sign a noninterest-bearing
note of $60,500 with payment due in two years.
Present
value
Future value
$60,500
?
End of
year 2
n = 2, i = 10%
To find the PV of the note (price of the shoes), we need to know
either the cash price of the shoes or the appropriate interest rate for
a transaction like this one. Let’s say the market rate is 10%.
LO6-4
Valuing a Note: One Payment, No Explicit
Interest
$60,500 (future value) × .82645* = $50,000 (present value)
*Present value of $1; n = 2, i = 10%
Concept Check √
Turp and Tyne Distillery is considering investing in a two-year project. The
company’s required rate of return is 10%. The present value of $1 for one
period at 10% is .909 and .826 for two periods at 10%. The project is
expected to create cash flows, net of taxes, of $240,000 in the first year,
and $300,000 in the second year. The distillery should invest in the project
if the project's cost is less than or equal to:
a.
$540,000
b.
$490,860
c.
$465,960
d.
$446,040
$218,160 ($240,000 x 0.909)
247,800 ($300,000 x 0.826)
$465,960
LO6-4
Expected Cash Flow Approach
Statement of Financial Accounting Concepts No. 7
(SFAC No. 7)
• Provides a framework for using future cash flows in
accounting measurement when uncertainty is
present.
• The objective in valuing an asset or liability using
present value is to approximate fair value of that
asset or liability
o Key to that objective is determining the present
value of future cash flows, taking into account any
uncertainty concerning the amounts and timing of
the cash flows
LO6-4
Illustration: Expected Cash Flow Approach
LDD Corporation faces the likelihood of having to pay an uncertain amount in five years
in connection with an environmental cleanup. Calculate the expected cash flow. Also
calculate the present value of the expected cash flow if the company’s credit-adjusted
risk-free rate of interest is 5%. The future cash flow estimate is in the range of $100
million to $300 million with the following estimated probabilities:
Loss Amount
Probability
$100 million
10%
$200 million
60%
$300 million
30%
The expected cash flow:
$100
200
300
X
X
X
10%
60%
30%
=
=
=
$ 10
120
90
$220
million
million
million
million
Present value of expected cash flows:
$220,000,000 X .78353 = $172,376,600
Present value of $1:
n = 5, i = 5%
Concept Check √
Willie Winn Track Shoes used the expected cash flow approach to
determine the present of a future obligation to be paid to Betty Will
Company in four years. Estimated future payment possibilities were as
follows:
Possible payment
Probability
$100 million
20%
140 million
40%
180 million
40%
The risk-free interest rate is 5%. The present value of $1 in 4 periods at 5%
is 0.82270. What is the estimated present value of the future obligation?
a. $115 million.
$100 million x 0.20 =
$ 20 million
$140 million x 0.40 =
56 million
b. $122 million.
$180 million x 0.40 =
72 million
c. $140 million.
$148 million
d. $148 million.
x .82270
$121.76 million
LO6-5
Basic Annuities
Annuity
• Series of cash flows of same amount received or
paid each period
Example:
A loan on which periodic interest is paid in equal amounts
Ordinary Annuity
• Cash flows occur at the end of each period
Annuity Due
• Cash flows occur at the beginning of each period
LO6-5
Ordinary Annuity
Example:
An installment note payable dated December 31, 2016,
might require the debtor to make three equal annual
payments, with the first payment due on December 31,
2017, and the last one on December 31, 2019.
LO6-5
Annuity Due
Example:
A three-year lease of a building that begins on December
31, 2016, and ends on December 31, 2019, may require
the first year’s lease payment in advance on December
31, 2016. The third and last payment would take place on
December 31, 2018, the beginning of the third year of the
lease.
Concept Check √
Justin Investor wants to calculate how much money he needs to deposit
today into a savings account that earns 4% in order to be able to withdraw
$6,000 at the end of each of the next 5 years. He should use which present
value concept?
a.
Present value of $1 for 5 periods.
b.
Present value of an annuity due of $1 for 5 periods.
c.
Present value of an ordinary annuity of $1 for 5 periods.
d.
Future value of $1 for 5 periods.
The calculation is how much needs to be deposited today, the present
value, so that equal amounts can be withdrawn over the next six years
at the end of the year (ordinary annuity).
Concept Check √
The Knotworth Gedding Consulting Company purchased a machine for
$15,000 down and $500 a month payable at the end of each of the next 36
months. How would the company calculate the cash price of the machine,
assuming the annual interest rate is known?
a. $15,000 plus the present value of $18,000 ($500 x 36).
b. $15,000 plus the present value of an annuity due of $500 for 36
periods.
c. $33,000.
d. $15,000 plus the present value of an ordinary annuity of $500 for 36
periods.
The cash price is equal to the present value of the future cash outflows.
This includes the $15,000 today plus the value today, present value, of
the $500 payments made at the end of each month (ordinary annuity).
Concept Check √
If you have a set of present value tables, an annual interest rate, the dollar
amount of equal payments made, and the number of semiannual
payments, what other information do you need to calculate the present
value of the series of payments?
a.
The rate of inflation.
b.
The timing of the payments (whether they are at the beginning or end
of the period).
c.
The future value of the annuity.
d.
No other information is needed.
If the payments are made at the end of each period, it
is an ordinary annuity. If the payments are made at
the beginning of each period, it is an annuity due.
LO6-6
Future Value of an Ordinary Annuity
Sally Rogers wants to accumulate a sum of money to pay for graduate school. Rather
than investing a single amount today that will grow to a future value, she decides to
invest $10,000 a year over the next three years in a savings account paying 10% interest
compounded annually. She decides to make the first payment to the bank one year
from today.
FV of $1
i = 10%
Payment
First payment
Second payment
Third payment
Total
$10,000
10,000
×
10,000
×
×
1.21
1.10
1.00
3.31
Future value
(at the end of year 3)
n
=
$12,100
2
=
11,000
=
10,000
$33,100
1
0
LO6-6
Using the FVA Table to Calculate the Future Value
FVA = $10,000 (annuity amount) × 3.31* = $33,100
*Future value of an ordinary annuity of $1: n = 3, i =10%
LO6-6
Future Value of an Annuity Due
FV of $1
i = 10%
Payment
First payment
Second payment
Third payment
Total
$10,000
10,000
×
10,000
×
×
1.331
1.210
1.100
3.641
Future value
(at the end of year 3)
n
=
$13,310
3
=
12,100
=
11,000
$36,410
2
1
Easier way:
FVA = $10,000 (annuity amount) × 3.641* = $36,410
*Future value of an ordinary annuity of $1: n = 3, i =10%
LO6-7
Present Value of an Ordinary Annuity
Sally wants to accumulate a sum of money to pay for graduate school. She wants to
invest a single amount today in a savings account earning 10% interest compounded
annually that is equivalent to investing $10,000 at the end of each of the next three
years.
PV of $1
Present value
i = 10% (at the beginning of the year 1)
Payment
First payment
Second payment
Third payment
Total
$10,000
10,000
×
10,000
×
×
.90909
.82645
.75131
2.48685
n
=
$9,091
1
=
8,264
=
7,513
$24,868
2
3
LO6-7
Using the PVA Table to Calculate the Present Value
PVA = $10,000 (annuity amount) × 2.48685* = $24,868
LO6-7
Present Value of an Annuity Due
In the previous illustration, suppose that the three equal payments of $10,000 are to
be made at the beginning of each of the three years. What is the present value of this
annuity?
Payment
First payment
Second payment
Third payment
Total
PV of $1
Present value
i = 10% (at the beginning of the year 1)
$10,000
=
1.00000
$10,000
10,000
×
.90909
=
9,091
10,000
×
.82645
2.73554
=
8,264
$27,355
×
n
0
1
2
LO6-7
Using the PVAD Table to Calculate the Present Value
PVA= $10,000 (annuity amount) × 2.73554* = $27,355
*Present value of an annuity due of $1: n = 3, i = 10%
From Table 6
Concept Check √
The Stinch Fertilizer Corporation wants to accumulate $8,000,000 for plant
expansion. The funds are needed on January 1, 2021. Stinch intends to make
five equal annual deposits in a fund that will earn interest at 7% compounded
annually. The first deposit is to be made on January 1, 2016. Present value and
future value facts are as follows:
Future value of an ordinary annuity of $1 at 7% for 5 periods
5.75
Future value of an annuity due of $1 at 7% for 5 periods
6.15
Present value of $1 at 7% for 5 periods
.713
Present value of an ordinary annuity of $1 at 7% for 5 periods 4.10
What is the amount of the required annual deposit?
a.
$1,300,813
$8,000,000  6.15 * = $1,300,813
b.
$1,391,304
c.
d.
$1,951,220
$1,704,000
*Future value of an annuity due of $1 at 7% for 5 periods)
Concept Check √
I. R. Wright plans to make quarterly deposits of $200 for 5 years into a
savings account. The first deposit will be made immediately. The savings
account pays interest at an annual rate of 8%, compounded quarterly. How
much will Wong have accumulated in the savings account at the end of the
five-year period?
Future value of an ordinary annuity of $1 at 8% for 5 periods
6.3359
Future value of an annuity due of $1 at 8% for 5 periods
5.8666
Future value of an ordinary annuity of $1 at 2% for 20 periods
26.1833
Future value of an annuity due of $1 at 2% for 20 periods
24.2974
a.
$2,672
b.
$4,000
c.
$4,860
d.
$5,237
$200 x 24.2974* = $4,860
*future value of an annuity due for 20 periods at 2%
Concept Check √
U. B. Wong plans to make quarterly deposits of $200 for 5 years into a
savings account. The deposits will be made at the end of each quarter. The
savings account pays interest at an annual rate of 8%, compounded
quarterly. How much will Wong have accumulated in the savings account at
the end of the five-year period?
Future value of an ordinary annuity of $1 at 8% for 5 periods
6.3359
Future value of an annuity due of $1 at 8% for 5 periods
5.8666
Future value of an ordinary annuity of $1 at 2% for 20 periods
26.1833
Future value of an annuity due of $1 at 2% for 20 periods
24.2974
a.
$2,672
b.
$4,000
c.
$4,860
d.
$5,237
$200 x 26.1833* = $5,237
*future value of an ordinary annuity for 20 periods at 2%
LO6-7
Present Value of a Deferred Annuity
Deferred annuity:
• Exists when the first cash flow occurs more than one
period after the date the agreement begins
At January 1, 2016, you are considering acquiring an investment that will
provide three equal payments of $10,000 each to be received at the end of
three consecutive years. However, the first payment is not expected until
December 31, 2018. The time value of money is 10%. How much would you be
willing to pay for this investment?
LO6-7
Present Value of a Deferred Annuity (continued)
At January 1, 2016, you are considering acquiring an investment that will
provide three equal payments of $10,000 each to be received at the end of
three consecutive years. However, the first payment is not expected until
December 31, 2018. The time value of money is 10%. How much would you be
willing to pay for this investment?
PV of $1
i = 10%
Payment
First payment
Second payment
Third payment
Total
$10,000
10,000
10,000
Present value
=
$7, 513
×
.75131
.68301
=
6,830
×
.62092
=
6,209
$20,552
×
n
3
4
5
LO6-7
Present Value of a Deferred Annuity
Alternative: Two-Step Process
1. Calculate the PV of the annuity as of the beginning of
the annuity period.
2. Reduce the single amount calculated in (1) to its
present value as of today.
Illustration:
LO6-7
Present Value of a Deferred Annuity—Two-Step Process
(continued)
Step 1:
PVA= $10,000 (annuity amount) × 2.48685* = $24,868
*Present value of an ordinary annuity of $1: n = 3, i = 10%*
Step 2:
PV = $24,868 (future amount) × .82645* = $20,552
*Present value of $1: n = 2, i = 10%*
Concept Check √
Harry Byrd’s Chicken Shack agrees to pay an employee $50,000 a year for
six years beginning two years from today and decides to fund the payments
by depositing one lump sum in a savings account today. The company
should use which present value concept to determine the required deposit?
a.
Future value of $1.
b.
Future value of a deferred annuity.
c.
Present value of a deferred annuity.
d.
None of the above.
The calculation is the amount to be deposited today, the
present value, of six equal payments (an annuity), that
doesn’t start for two years (deferred annuity).
LO6-7
Financial Calculators
Texas Instruments model BA-35 has:
Example:
• Assume you need to determine the present value of a 10period ordinary annuity of $200 using a 10% interest rate.
• Enter N to be 10, %I to be 10, and PMT to be −200,
then press CPT and PV to obtain the answer of
$1,229.
LO6-7
Excel
• We can use spreadsheet software, such as Excel, to
solve time value of money problems.
• Excel has a function called PV that calculates the
present value of an ordinary annuity.
• To use the function, you would select the pull-down
menu for “Insert,” click on “Function” and choose the
category called “Financial.” Scroll down to PV and
double-click.
• Then input the necessary variables—interest rate,
the number of periods, and the payment amount.
LO6-8
Solving for Unknown Values in Present Value Situations
Determining the Annuity Amount when Other Variables are
Known
$700 (present value) = 3.31213* × annuity amount
$700 (present value) ÷ 3.31213* = $211.34 (annuity amount)
* Present value of an ordinary annuity of $1: n = 4, i = 8%
LO6-8
Solving for Unknown Values in Present Value Situations
Determining the Unknown Number of Periods—Ordinary Annuity
$700 (present value) = $100 (annuity amount) × ?*
* Present value of an ordinary annuity of $1: n = ?, i = 7%
PVA table factor
$700 (present value) ÷ $100 (annuity amount) = 7.0000*
* Present value of an ordinary annuity of $1: n = ?, i = 7%
In the PVA table (Table 4), search the 7% column ( i = 7%) for this value and
find 7.02358 in row 10. So it would take about 10 years to repay the loan.
LO6-8
Solving for Unknown Values in Present Value Situations
Determining i When Other Variables Are Known
$331(present value) = $100 (annuity amount) × ?*
* Present value of an ordinary annuity of $1: n = 4, i = ?
PVA table factor
$331 (present value) ÷ $100 (annuity amount) = 3.31*
* Present value of an ordinary annuity of $1: n = 4, i = ?
In the PVA table (Table 4), search row four (n = 4) for 3.31. We find it
in the 8% column. So the effective interest rate is 8%.
LO6-8
Determining i When Other Variables Are
Known— Unequal Cash Flows
$400 (present value) =
$100 (annuity amount) × PVA* + $200 (single payment) × PV†
* Present value of an ordinary annuity (PVA) of $1: n = 3, i = ?
† Present value (PV) of $1: n = 4, i = ?
Using i = 9%
PV = $100 (2.53129)* + $200 (.70843)† = $395
Using i = 8%
PV = $100 (2.57710)* + $200 (.73503)† = $405
$400
This indicates that the interest rate implicit in the agreement is about 8.5%.
Concept Check √
The Omagosh Company purchased office furniture for $25,800 and agreed
to pay for the purchase by making five annual installment payments
beginning one year from today. The installment payments include interest
at 8%. The present value of an ordinary annuity for 5 periods at 8% is
3.99271. The present value of an annuity due for 5 periods at 8% is
4.31213. What is the required annual installment payment?
a. $5,160
b. $6,462
c. $5,982
d. $4,398
$25,800  3.99271* = $ 6,462
*present value of an ordinary annuity for 5 periods at 8%
LO6-9
Valuing a Long-Term Bond Liability
On June 30, 2016, Fumatsu Electric issued 10% stated rate bonds with a face
amount of $200 million. The bonds mature on June 30, 2036 (20 years). The
market rate of interest for similar issues was 12%. Interest is paid
semiannually (5%) on June 30 and December 31, beginning December 31,
2016. The interest payment is $10 million (5% X $200 million).
What was the price of the bond issue? What amount of interest expense will
Fumatsu record for the bonds in 2016?
Present value of an ordinary annuity of $1: n = 40, i = 6%
PVA = $10 million (annuity amount) X 15.04630 = $150,463,000
PV = $200 million (lump-sum) X .09722 =
19,444,000
Price of the bond issue = $169,907,000
Present value of $1: n = 40, i = 6%
Interest expense =
$169,907,000 × 6% = $10,194,420
LO6-9
Valuing a Long-Term Lease Liability
On January 1, 2016, the Stridewell Wholesale Shoe Company signed a 25-year
lease agreement for an office building. Terms of the lease call for Stridewell to
make annual lease payments of $10,000 at the beginning of each year, with
the first payment due on January 1, 2016. Assuming an interest rate of 10%
properly reflects the time value of money in this situation, how should
Stridewell value the asset acquired and the corresponding lease liability?
PVAD = $10,000 (annuity amount) × 9.98474 = $99,847
Present value of an annuity due of $1: n = 25, i =10%
Journal Entry
Debit
Leased office building
Lease payable
99,847
Credit
99,847
Concept Check √
On March 31, 2016, the Gusto Beer Company leased a machine from B. A.
Lush, Inc. The lease agreement requires Gusto to pay 8 annual payments of
$16,000 on each May 31, with the first payment due on May 31, 2016.
Assuming an interest rate of 6% and that this lease is treated as an
installment sale (capital lease), Gusto will initially value the machine by
multiplying $16,000 by which of the following?
a.
Present value of $1 at 10% for 6 periods.
b.
Present value of an ordinary annuity of $1 at 10% for 6 periods.
c.
Present value of an annuity due of $1 at 10% for 6 periods.
d.
Future value of an annuity due of $1 at 10% for 6 periods.
Present value of an annuity due of $1 at 10% for 6 periods.
The calculation is how much is recorded today, the present
value of equal payments that start today (annuity due).
LO6-9
Valuing a Pension Obligation
On January 1, 2016, the Stridewell Wholesale Shoe Company hired Sammy Sossa.
Sammy is expected to work for 25 years before retirement on December 31, 2040.
Annual retirement payments will be paid at the end of each year during his retirement
period, expected to be 20 years. The first payment will be on December 31, 2041.
During 2016 Sammy earned an annual retirement benefit estimated to be $2,000 per
year. The company plans to contribute cash to a pension fund that will accumulate to
an amount sufficient to pay Sammy this benefit. Assuming that Stridewell anticipates
earning 6% on all funds invested in the pension plan, how much would the company
have to contribute at the end of 2016 to pay for pension benefits earned in 2016?
This is a
deferred annuity.
Present value of an ordinary
annuity of $1: n = 20, i = 6%
PVA = $2,000 (annuity amount) X 11.46992 =
$22,940
$5,666
PV = $22,940 (future amount) X .24698 =
Present value of $1: n = 24, i = 6%
Summary of Time Value of Money Concepts
End of Chapter 6