nAME:
id:
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* 1. Find the future value of $10,000 invested now after five years if the annual interest rate is 8 percent. *
* a. What would be the future value if the interest rate is a simple interest rate? *
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* b. What would be the future value if the interest rate is a compound interest rate?

* 2.Find the present value of $7,000 to be received one year from now assuming a 3 percent annual discount interest rate. Also calculate the present value if the $7,000 is received after two years. *

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3. Determine the future value at the end of two years of an investment of $3,000 made now and an additional $3,000 made one year from now if the compound annual interest rate is 4 percent.

4. Determine the present value now of an investment of $3,000 made one year from now and an additional $3,000 made two years from now if the annual discount rate is 4 percent.

5.What is the present value of a loan that calls for the payment of $500 per year for six years if the discount rate is 10 percent and the first payment will be made one year from now? How would your answer change if the $500 per year occurred for ten years?

6. a. What is the annual percentage rate (APR) on a loan that charges interest of .75 percent per month?

b. What is the effective annual rate (EAR) on the loan described in (a)?

...TimeValue of Money
A dollar received today is worth more
than a dollar received in the future
TimeValue of Money
1
Compounding And Future Value
1.
2.
3.
Simple Interest occurs when interest is earned only on the
initial investment
Compound Interest occurs when interest paid on the
investment during the first period is added to the principal;
then, during the second period, interest is earned on this new
sum.
For example, we place RM100 in a savings account that
pays 6% interest, compounded annually. At the end of the
first year, we have earned 6%, or RM6 on the initial deposit
of RM100, giving us a total of RM106.
TimeValue of Money
2
Compounding And Future Value
4.
The mathematical formula is FV1 = PV(1 + i)
5.
At the end of year 2, we now earn 6% interest on the
principal of RM106; FV2 = 106 (1 + 0.06) = RM112.36
6.
At the end of year 3, we now earn 6% interest on the
principal of RM112.36; FV3 = 112.36(1+ 0.06) ==
RM119.10
The value of investment if it is compounded annually at a
rate of i for n years is FVn = PV(1 + i)n
7.
TimeValue of Money
3
EXAMPLE 1
If
we place RM1000 in a savings account paying 5% interest
compounded annually, how much will our account accrue to in
10 years?
Answer:
FV10 = 1000(1 + 0.05)10
= 1000(1.62889)
= RM1,628.89
Thus, at the end of 10 years, we will have...

...
TIMEVALUE OF MONEY (CHAPTER 4)
1. Future value (FV), the value of a present amount at a future date, is calculated by applying compound interest over a specific time period. Present value (PV), represents the dollar value today of a future amount, or the amount you would invest today at a given interest rate for a specified time period to equal the future amount. Financial managers prefer present value to future value because they typically make decisions at time zero, before the start of a project.
2. A single amount cash flow refers to an individual, stand alone, value occurring at one point in time. An annuity consists of an unbroken series of cash flows of equal dollar amount occurring over more than one period. A mixed stream is a pattern of cash flows over more than one time period and the amount of cash associated with each period will vary.
3. Compounding of interest occurs when an amount is deposited into a savings account and the interest paid after the specified time period remains in the account, thereby becoming part of the principal for the following period. The general equation for future value in year n (FVn) can be expressed using the specified notation as follows:
FVn ’ PV × (1 + i)n
4. A decrease in the interest rate lowers...

...TIMEVALUE OF MONEY FORMULA SHEET
#
TVM Formula For:
1
Future Value of a
Lump Sum. (FVIFi,n)
Compounded/Payments
(m) Times per Year
Annual Compounding
FVn = PV( 1 + i )n
2
FV
1 i
PV =
Present Value of a
Lump Sum. (PVIFi,n)
-n
Future Value of an
Annuity. (FVIFAi,n)
FVAn = CF
4
Present Value of an
Annuity. (PVIFAi,n)
1 - ( 1 + i )-n
PVAn = CF
i
5
Present Value of
Perpetuity. (PVA )
6
Effective Annual Rate
given the APR.
7
The length of time
required for a PV to
grow to a FV.
8
The APR required for
a PV to grow to a FV.
9
Present Value of
a Growing Annuity.
10
Present Value of
a Growing
Perpetuity.
11
The length of time
required for a series
of PMT’s to grow to a
future amount (FVAn).
12
EAR = APR
n=
(-m n)
m
-1
ln ( FV/PV)
m ln (1 i/m)
FV
PV
i= m
EAR = ei - 1
n=
ln (FV/PV)
i
i=
ln (FV/PV)
n
[1/(m n)]
-1
n
(FVA)(i)
+1
CF
ln (1 + i)
ln 1
n
n=
(1/n)
1 g
1 i
(-i n)
CF0 1 g
i g
PVA
ln
i
EAR = 1
m
-1
PV = FV e
CF
[(1 i/m) m 1]
PVA
i
CF0 1 g
1
i g
PVAn
1 - 1 + i/m
PVAn = CF
i/m
ln (FV/PV)
ln (1 + i )
FV
i=
PV
(-m n)
( 1 + i/m )(m n) - 1
i/m
FVAn = CF
CF
i
FV
(i...

...Why is the timevalue of money concept important? In what quantitative decisions might the timevalue of money be used? How do you apply the timevalue of money concept to make decisions in your personal life?
The idea of the timevalue of money is important because of the fundamental assertion that one would rather have X number of dollars now, than later. If the money is taken later a value of X+i is preferred. This concept is applied to all situations where someone uses the monies of another for some duration of time and is expected to return the money. This is used in loans, savings accounts, investments, annuities, etc... I apply the timevalue of money in my personal life in many ways. I calculated out a couple payment options for the new vehicle I purchased this year to see which one cost the least in the end. I also had to figure out how much I had to put in my sons’ college savings fund so it would be worth a certain amount when they turn 18. That was just this year. This concept is widely used in important areas of our personal finances.
How might you use the TimeValue of Money concept as a quantitative reasoning tool in business?
In business you need to take out loans to expand or in times of shortage. It is important to understand the...

...how much money will be in your account after 5 years?
2. What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.
3. If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?
4. Your parents are planning to retire in 18 years. They currently have $250,000 and they would like to have $1,000,000 when they retire. What annual rate of interest would they have to earn on their $250,000 in order to reach their goal, assuming they save no more money?
5. What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent.
6. What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year.
7. While you were a student in college, you borrowed $12,000 in student loans at an interest rate of 9 percent, compounded annually. If you repay $1,500 per year, how long, to the nearest year, will it take you to repay the loan?
8. What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7 percent? If interest rates in general were to double and the appropriate discount rate rose to 14 percent, what would happen to the present value...

...Calculate the Terminal Value
Having estimated the free cash flow produced over the forecast period, we need to come up with a reasonable idea of the value of the company's cash flows after that period - when the company has settled into middle-age and maturity. Remember, if we didn't include the value of long-term future cash flows, we would have to assume that the company stopped operating at the end of the five-year projection period.
The trouble is that it gets more difficult to forecast cash flows over time. It's hard enough to forecast cash flows over just five years, never mind over the entire future life of a company. To make the task a little easier, we use a "terminal value" approach that involves making some assumptions about long-term cash flow growth.
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Gordon Growth Model
There are several ways to estimate a terminal value of cash flows, but one well-worn method is to value the company as a perpetuity using the Gordon Growth Model. The model uses this formula:
Terminal Value = Final Projected Year Cash Flow X (1+Long-Term Cash Flow Growth Rate)
(Discount Rate – Long-Term Cash Flow Growth Rate)
The formula simplifies the practical problem of projecting cash flows far into the future. But keep in mind that the formula rests on the big assumption...

...Gayle M. Doria Finance21
Prof. Khen Enriquez
This article will explain the financial concept of timevalue of money. The overview provides an introduction to the principles at work when money grows in value over time. These principles include future value of money, present value of money, simple interest and compound interest. In addition, other concepts that relate to factors that can impede the growth in value of money over time are explained, including risk, inflation and accessibility of assets. Basic formulas and tables have been provided to assist in calculating various formulations of timevalue of money problems. Explanations of common financial dealings in which the timevalue of money is an important consideration, such as annuities, loan amortization and tax deferral options, are included to help illustrate the concept of the timevalue of money in everyday life.
The timevalue of money is a fundamental financial principle. Its basic premise is that money gains value over time. As a result, a dollar saved today will be worth more in the future, and a dollar paid today costs more than a dollar paid later in time. The reason for the increasing value in money over...