PART 1:FINANCIAL PLANNING

Chapter 3Chapter 3

Understanding the Time Understanding the Time Value of MoneyValue of Money

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Compound Interest andCompound Interest andFuture ValuesFuture Values

Compound interest is interest paid on Compound interest is interest paid on interest.interest.

If you take interest earned on an If you take interest earned on an investment and reinvest it, you earn investment and reinvest it, you earn interest on the principal and the interest on the principal and the reinvested interest. reinvested interest.

The amount of interest earned annually The amount of interest earned annually increases each year because of increases each year because of compounding. compounding.

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How Compound Interest How Compound Interest WorksWorks

How does $100 How does $100 placed in a savings placed in a savings account at 6% grow account at 6% grow at the end of the 1at the end of the 1stst and 2and 2ndnd years? years?

End of 1End of 1stst year = year = $106$106

End of 2End of 2ndnd year = year = $112.36$112.36

The amount of The amount of interest earned interest earned annually increases annually increases each year because each year because of compounding.of compounding.

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How Compound Interest How Compound Interest WorksWorks

Example: You Example: You receive a $1000 receive a $1000 academic award this academic award this year for being the year for being the best student in your best student in your personal finance personal finance course. You place it course. You place it in a savings account in a savings account paying 5% interest paying 5% interest compounded compounded annually. How much annually. How much will your account be will your account be worth in 10 years? worth in 10 years?

$1628.89$1628.89

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The Future-Value The Future-Value Interest FactorInterest Factor

Calculating future values by Calculating future values by hand can be difficult.hand can be difficult.

Use a calculator or tables.Use a calculator or tables.

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The Future-Value The Future-Value Interest FactorInterest Factor

The amounts in the table represent The amounts in the table represent the value of $1 compounded at rate the value of $1 compounded at rate of of i i at the end of at the end of nnth year.th year.

FVIFFVIFi, n i, n is multiplied by the initial is multiplied by the initial investment to calculate the future investment to calculate the future value of that investment.value of that investment.

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The Future-Value The Future-Value Interest FactorInterest Factor

Previous example: Previous example: What is the future What is the future value of investing value of investing $1000 at 5% $1000 at 5% compounded compounded annually for 10 annually for 10 years? years?

Using Table 3.1, Using Table 3.1, look for the look for the intersection of the intersection of the nn = 10 row and the = 10 row and the 5% column. 5% column.

The FVIF = 1.629The FVIF = 1.629 $1000 x 1.629 = $1000 x 1.629 =

$1629$1629

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The Rule of 72The Rule of 72

How long will it take to double your How long will it take to double your money? money?

The Rule of 72 determines how The Rule of 72 determines how many years it will take for a sum to many years it will take for a sum to double in value by dividing the double in value by dividing the annual growth or interest rate into annual growth or interest rate into 72. 72.

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The Rule of 72The Rule of 72

Example: If an investment grows at an Example: If an investment grows at an annual rate of 9% per year, then it annual rate of 9% per year, then it should take 72/9 = 8 years to double. should take 72/9 = 8 years to double.

Use Table 3.1 and the future-value Use Table 3.1 and the future-value interest factor: The FVIF for 8 years at interest factor: The FVIF for 8 years at 9% is 1.993 (or $1993), nearly the 9% is 1.993 (or $1993), nearly the approximated 2 ($2000) from the Rule approximated 2 ($2000) from the Rule of 72 method. of 72 method.

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Compound Interest with Compound Interest with Nonannual PeriodsNonannual Periods

Compounding periods may not always be Compounding periods may not always be annually. annually.

Compounding may be quarterly, monthly, Compounding may be quarterly, monthly, daily, or even a continuous basis. daily, or even a continuous basis.

The sooner interest is paid, the sooner The sooner interest is paid, the sooner interest is earned on it, and the sooner the interest is earned on it, and the sooner the benefits or compounding is realized. benefits or compounding is realized.

Money grows faster as the compounding Money grows faster as the compounding period becomes shorter.period becomes shorter.

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Compounding and theCompounding and thePower of TimePower of Time

Manhattan was purchased in 1626 Manhattan was purchased in 1626 for $24 in jewelry and trinkets. for $24 in jewelry and trinkets.

Had that $24 been invested at 8% Had that $24 been invested at 8% compounded annually, it would be compounded annually, it would be worth over $120.6 trillion today.worth over $120.6 trillion today.

This illustrates the incredible power This illustrates the incredible power of time in compounding.of time in compounding.

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The Importance of theThe Importance of theInterest RateInterest Rate

The interest rate plays a critical role in The interest rate plays a critical role in how much an investment grows. how much an investment grows.

Albert Einstein called compound Albert Einstein called compound interest “the eighth wonder of the interest “the eighth wonder of the world.” world.”

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Present ValuePresent Value

Present value is the value of today’s Present value is the value of today’s dollars of money to be received in dollars of money to be received in the future. the future.

Allows comparisons of dollar values Allows comparisons of dollar values from different periods.from different periods.

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Present ValuePresent Value

Finding present values means Finding present values means moving future money back to the moving future money back to the present.present.

The “discount rate” is the interest The “discount rate” is the interest rate used to bring future money rate used to bring future money back to present.back to present.

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Present ValuePresent Value

Tables or a financial calculator can Tables or a financial calculator can be used to calculate present value.be used to calculate present value.

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Present ValuePresent Value

Example: What is Example: What is the present value the present value of $100 to be of $100 to be received 10 years received 10 years from now if the from now if the discount rate is discount rate is 6%? 6%?

Using Table 3.3, Using Table 3.3, n n = = 10 row and 10 row and i i = 6% = 6% column, the PVIF is column, the PVIF is 0.558. 0.558. Insert Insert FVFV10 10 = $100 and = $100 and

PVIF PVIF 6%, 10 yr6%, 10 yr = 0.558 = 0.558 into the equation.into the equation.

The value in today’s The value in today’s dollars of $100 future dollars of $100 future dollars is $55.80.dollars is $55.80.

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Present ValuePresent Value

Example: You Example: You have been have been promised promised $500,000 $500,000 payable 40 payable 40 years from years from now. What is now. What is the value the value today if the today if the discount rate discount rate is 6%? is 6%?

PV PV = = FVFVnn((PVIFPVIF i%, i%, nn yrs yrs)) Using Table 3.3, Using Table 3.3, nn = 40 = 40

row and row and i i = 6% = 6% column, the PVIF is column, the PVIF is 0.097. 0.097. Multiply the $500,000 by Multiply the $500,000 by

0.097.0.097. The value in today’s The value in today’s

dollars is $48,500.dollars is $48,500.

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Present ValuePresent Value You’ve just seen that $500,000 payable You’ve just seen that $500,000 payable

40 years from now, with a discount rate 40 years from now, with a discount rate of 6%, is worth $48,500 in today’s of 6%, is worth $48,500 in today’s dollars. dollars.

Conversely, if you deposit $48,500 in the Conversely, if you deposit $48,500 in the bank today, earning 6% interest bank today, earning 6% interest annually, in 40 years you would have annually, in 40 years you would have $500,000.$500,000.

There is really only one time value There is really only one time value money equation. money equation.

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AnnuitiesAnnuities

An annuity is a series of equal dollar An annuity is a series of equal dollar payments coming at the end of each payments coming at the end of each time period for a specific time time period for a specific time period.period.

Pension funds, insurance Pension funds, insurance obligations, and interest received obligations, and interest received from bonds are annuities.from bonds are annuities.

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Compound AnnuitiesCompound Annuities

A compound annuity involves A compound annuity involves depositing an equal sum of money at depositing an equal sum of money at the end of each year for a certain the end of each year for a certain number of years, allowing it to grow.number of years, allowing it to grow.

Constant periodic payments may be Constant periodic payments may be for an education, a new car, or any for an education, a new car, or any time you want to know how much time you want to know how much your savings will have grown by your savings will have grown by some point in the future.some point in the future.

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Compound AnnuitiesCompound Annuities

Example: You Example: You deposit $500 deposit $500 at the end of at the end of each year for each year for the next 5 the next 5 years. If the years. If the bank pays 6% bank pays 6% interest, how interest, how much will you much will you have at the have at the end of 5 years? end of 5 years?

Future value of an Future value of an annuity = annual annuity = annual payment x future value payment x future value interest factor of an interest factor of an annuity.annuity.

Use Table 3.5, column Use Table 3.5, column ii = = 6%, row 6%, row nn = 5, the FVIFA = 5, the FVIFA is 5.637.is 5.637.

$500 x 5.637 = $2,818.50 $500 x 5.637 = $2,818.50 at the end of 5 years.at the end of 5 years.

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Compound AnnuitiesCompound Annuities Example: You Example: You

need $10,000 need $10,000 for education for education in 8 years. in 8 years. How much How much must you put must you put away at the away at the end of each end of each year at 6% year at 6% interest to interest to have the have the college money college money available? available?

You know the values of You know the values of nn, , ii, and , and FVFVnn, but don’t , but don’t know the know the PMTPMT. .

You must deposit You must deposit $1010.41 at the end of $1010.41 at the end of each year at 6% interest each year at 6% interest to accumulate $10,000 at to accumulate $10,000 at the end of 8 years.the end of 8 years.

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Present Value of an Present Value of an AnnuityAnnuity

To compare the relative value of To compare the relative value of annuities, you need to know the annuities, you need to know the present value of each.present value of each.

Use the present-value interest factor Use the present-value interest factor for an annuity for an annuity PFIVAPFIVAi,ni,n..

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Present Value of an Present Value of an AnnuityAnnuity

Example: You Example: You are to receive are to receive $1,000 at the $1,000 at the end of each year end of each year for the next 10 for the next 10 years. If the years. If the interest rate is interest rate is 5%, what is the 5%, what is the present value?present value?

Using Table 3.7, Using Table 3.7, row row n n = 10, = 10, i i = 5%. = 5%.

The present value The present value of this annuity is of this annuity is $7722.$7722.

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Amortized LoansAmortized Loans

Annuities usually involve paying off a Annuities usually involve paying off a loan in equal installments over time.loan in equal installments over time.

Amortized loans are paid off this way. Amortized loans are paid off this way. The interest payment declines each The interest payment declines each

year as the loan outstanding declines.year as the loan outstanding declines. Examples include car loans and Examples include car loans and

mortgages.mortgages.

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PerpetuitiesPerpetuities A perpetuity is an annuity that A perpetuity is an annuity that

continues forever. continues forever. Every year this investment pays Every year this investment pays

the same dollar amount and never the same dollar amount and never stops paying. stops paying.