Time Value of Money

16 Pages

Financial Accounting
Course Code
Liang Chen

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Introductory Financial Accounting Time Value of MoneyAccountingBusiness Applications If someone were to ask you if you would rather have 100 today or 100 next year your answer would be Id like the 100 todayYour answer is based on the time value of moneyThe difference between the worth of the two amounts is interestMany accounting and business applications use the time value of moneyThese applications include accounting for bonds leases notes and pensionsExamples of business applications include what rate of return is acceptable for investment and what interest rate to charge credit customersThere are numerous personal applications as well such as the purchase of a home vs renting whether to borrow for or lease a new car and retirement planningLets say that you would like to do a little retirement planning and have decided you want to be a millionaire by age 60If you are 20 years old right now and the aftertax rate of return is 1 per month how much would you have to save per month to achieve your goalOnly 85 per monthThats allThe power of interest and time is on your side SimpleCompound InterestPayment for the use of someone elses money is called interest There are two types of interest simple and compound Generally interest is specified in terms of a percentage rate for a period of time usually a yearFor example interest at 10 means the annual cost of borrowing an amount of money called the principal is equal to 10 of that amountIf 10000 is borrowed for a period of one year at 10 annual interest the total to be repaid is 11000 10000 principal and 1000 interest Most transactions however involve compound interestCompound interest is the interest that accrues on both the principal and the past unpaid accrued interest There are four basic types of compound interest computations1Present value of a single sum due in the future 2Present value of an annuity a series of receipts or payments 3Future value of a single sum at compound interest 4Future value of an annuityThe easiest way to handle time value problems is to use a timeline to visualize the time periods and the movement back and forth of money amountsA timeline should be used for all but the very simplest problemsA timeline looks like this01345 nPeriod All receipts or payments should be placed on the time line and then the number of periods for movement forward or back can be countedUsually the present time is placed at period 0 but this can be adjusted depending on the question Future Value Prepared by Professor Sandra DagaPage 1 of 16Introductory Financial Accounting Time Value of MoneyAccountingBusiness ApplicationsFuture value is the amount to which a present given amount of money will grow should interest be charged or earned The calculation of this amount will require the following information1 amount of the investment which is the principal p 2 rate of interest rate of return i 3 number of time periods nFor example we might want to determine the amount of money that we will have in our bank savings account in 3 years should we deposit 1000 today at an annual interest rate of 6 if compounding is annual The timeline looks like this0123 1000 1000 x 106 10601060 x 106112360 112360 x 1061191The arithmetic determination would be as followsend of year 1 we will have 10001000 x 1061060 end of year 2 we will have 10601060 x 106112360 end of year 3 we will have 112360 112360 x 106119100The amount of 1191 is the future value of 1000 at 6 per year compounded annually for 3 yearsThis process can be shortened through the use of a formula as followsnFVP1iFor this example using the formula3FV1000 1061000 1191 1191 which agrees to the arithmetic solution Prepared by Professor Sandra DagaPage 2 of 16
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