Abstract
The first steps toward understanding the relationship between the value of dollars today and that of dollars in the future is by looking at how funds invested will grow over time. This understanding will allow one to answer such questions as; how much should be invested today to produce a specified future sum of money?

Time Value of Money
In most cases, borrowing money is not free, unless it is a fiver for lunch from a friend. Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of the amount borrowed per a period of time, usually one year. The current market rates are composed of three items. The Real Rate of Interest is what compensates lenders for postponing their own spending during the term of the loan. An Inflation Premium is added to offset the possibility that inflation may eat into the value of the money during the term of the loan. In addition, various Risk Premiums are added to compensate the lender for risky loans such as unsecured loans made to borrowers with questionable credit ratings or loans that the lender may not be able to easily resell. The first two components of the interest rate listed above, the real rate of interest and an inflation premium, together are referred to as the nominal risk-free rate. In the United States, the nominal risk-free rate is estimated by the rate of US Treasury bills. Simple interest is calculated on the original principal only. Interest from prior periods is not used in calculations for the following periods. Simple interest is normally used for a single period loan of less than a year, such as 30 or 60 days loans. The formula is: Simple Interest = p * i * n

where:
p = principal (original amount borrowed or loaned)
i = interest rate for one period
n = number of periods
Compound interest is calculated each period on the original principal and all interest accumulated during past periods. The interest rate normally is stated as a yearly rate....

...TIMEVALUE OF MONEYTimevalue of money is useful in making informed business decisions. For example the "net present value method" can be used to help decide the best alternative among multiple alternative uses of a firm or personal financial resources. By discounting various alternatives to their "present value" one can compare the alternatives. Timevalue of money can also answer such questions as what one's investment will be worth at a certain point of time in the future, assuming a certain interest rate. Timevalue of money can also be used to compute such useful information as car, mortgage and other loan payments. Another use of timevalue of money in accounting is reporting of certain long-term assets and liabilities.
Timevalue of money is based on the principle of compound interest. Each time there is a compounding period the new principal is increased by the interest from the previous period.
Converting Before Using the Tables
When using the tables, you may need to convert if, for example, in a lump sum situation there are more than one compounding periods in a year. Or you may need to convert (to monthly compounding) if, for...

...Chen Suiming
4385287
5.1 Money has a timevalue because a dollar in hand today is worth more than a dollar to be received in the future. This makes sense because if we had the dollar today, we could buy something with it or invest it and earn interest.
5.5 Compounding is the process by which interest earned on an investment is reinvested so that in future periods, interest is earned on the interest previously earned as well as the principal.
Discounting is the process by which the present value of future cash flows is obtained.
5.4 The future value equation is: FVn = PV * (1+i)n
Future value at the end of year 3 = $ 5000 * (1+0.105)3
= $ 6746. 163125
Alison Green can collect $ 6746.163125 in 3 years.
5.11 The present value equation is: PV = FVn(1+i)n
The loan = 7750(1+0.06)3
= 6507. 05
I am willing to lend my brother around $ 6507
5.15 According to the equation: PV = FVn(1+i)n
1+in = FVnPV
Therefore, 1+i2 = 15001300
(1 + i) = 1.074
i = 0.074 =7.4%
Because 7.4% > 6.5%, so I should go with bank.
5.27 According to the equation: FVn = PV * (1+i/m)m*n,
a. FV5 = 3500 * (1+0.089/12)12*5...

...Introduction
The timevalue of money is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. The timevalue of money can be defined as the value of money received today instead of in the future. This is based on the premise that cash in hand today is more valuable than the same amount in the future due to its capability of earning interest. For investors, this is single most important concept in the world of finance. This paper will discuss the different financial applications of the timevalue of money. This paper will also describe the components of interest and highlight various methods of calculating timevalue of money using different interest scenarios.
Financial Applications of the TimeValue of MoneyTimevalue of money has many useful applications. One of the most important uses is that it helps to measure the trade-off in spending and saving. This can have important consequences for your personal budgeting. If market interest rates are at 5%, one may decide that the timevalue of money is greater in the future, and...

...TimeValue of Money (TVM), developed by Leonardo Fibonacci in 1202, is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities.
TVM is based on the concept that a dollar today is worth more than a dollar in the future. That is mainly because money held today can be invested and earn interest.
A key concept of TVM is that a single sum of money or a series of equal, evenly-spaced payments or receipts promised in the future can be converted to an equivalent value today. Conversely, one can determine the value to which a single sum or a series of future payments will grow to at some future date.
The timevalue of money serves as the foundation for all other notions in finance. It impacts business finance, consumer finance and government finance. Timevalue of money results from the concept of interest.
Key Components of TimeValue of Money
Present Value is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate. The future amount can be a single sum that will be received at the end of the last period, as a...

...TimeValue of MoneyTimevalue of money is an amount of money available today can be safely invested to accumulate to a larger amount in the future.
Present value- an amount of money available today.
Future amount-amount receivable/payable at a future date
Relationship Between Present Values and Present Values
The difference between present value and future amount is the interest that is included in the future amount. It depends on two factors:
1. Rate of interest at which present value increases
2. Length of time over which interest accumulates
The basic concept of TimeValue of Money:
* A PV is always less than its future amount.
* A future amount is always greater than a present value
* A dollar available today is always worth more than a dollar that does not become available until a future date
* A dollar available at a future date is always worth less than a dollar that is available today
Future Value Concepts
Future Value of a Single amount
The future value of a single amount is the value at a future date of a given amount invested assuming compound interest.
Formula:
FV= p X (1+i)n
Where:
FV= future...

...TimeValue of Money
As the name suggests it implies money valued with reference to time which may be present or future. “Time” allows the prospect to earn interest and defer consumption.
Present Value (PV) – it means the current value of money in future measured at a particular interest rate.
Future Value (FV) – it means the value of present money at some point of time in future measured at a particular interest rate.
The value of dollar is more as of today than in future. This is due to the following reasons:
• Risk/Uncertainty about the receipt of money in future
• Preference for current consumption.
• Present money offers investment opportunities to earn additional cash flows. Example – If you offer someone $5000 today or $5000 after a year, he would prefer $5000 today as that money can then be invested and one can earn interest on it.
• At the time of inflation, the value of dollar as of date represents more purchasing power than the value of dollar after an year.
Concept of TimeValue of Money.
1. FV of a single cash flow.
2. FV of periodic cash flows.
3. PV of a single cash flow.
4. PV of a periodic cash flows.
1. FV of single cash...

...
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...

...TimeValue of Money Practice Problems − Solutions
Dr. Stanley D. Longhofer 1) Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest annually at the rate of 9 percent for seven years. a) How much will Jim have on deposit at the end of seven years? P/Y = 1, N = 7, I = 9, PV = 12,000, PMT = 0 ⇒ FV = $21,936.47 b) Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much would he have at the end of seven years? P/Y = 4, N = 7 × 4 = 28 ⇒ FV = $22,374.54 c) In comparing parts (a) and (b), what are the respective effective annual yields? Which alternative is better? Because interest in compounded annual in part (a), the effective annual rate is the same as the nominal rate: EARA = 9%. In part (b), EARB = (1 + i/m)m – 1 = 1.02254 – 1 = 9.31%. This can be also solved using the TI BAII+ using the Interest Conversion worksheet. Simply press [2nd] [I Conv] (the second function of the 2 key) to bring up this worksheet. When the screen says NOM = press [9] and [Enter]. Then arrow up and make sure that [C/Y] reads 4 compounding periods per year; if not, press [4] and [Enter]. Finally arrow up to the EFF screen and press [CPT] to compute the effective annual rate. Alternative (b) is preferred because it compounds your interest more frequently. Thus you get to earn “interest on your interest” sooner. 2) John is considering the purchase of a lot. He can buy the lot today and expects the...

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