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# Understanding and Benefiting from the Time Value of Money - PowerPoint PPT Presentation

Understanding and Benefiting from the Time Value of Money. Contents. Introductory applied questions Basic formulas and computations Present Value and Future Value Annuities Practical applications of Time Value Practice problems Website links. Money is worth more as time progresses

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### Understanding and Benefiting from the Time Value of Money

• Introductory applied questions

• Basic formulas and computations

• Present Value and Future Value

• Annuities

• Practical applications of Time Value

• Practice problems

Compounding opportunity creates the maximum value over a given period of time.

• Simply refers to interest earning interest

• Significantly influences how fast a dollar amount grows

• May be computed annually or more frequently, such as quarterly, monthly, daily, or continually

• \$1,000 x 10% = \$100 interest earned you have at the end of a year?

• Add \$1000 principle to \$100 interest

• Balance at end of first year is \$1,100

• Shortcut:

\$1,000 x 1.10 = \$1,100 Thus,

Present value (1 + interest rate) = Future Value

Shortcut you have at the end of a year?

• Check out a FVIF table and get factor for 1 year and 10% interest. Multiply this by the principle (PV) amount.

Thus the FV = PV x FVIF

Future Value Interest Factors you have at the end of a year?(1+I)n = FVIF

\$1,100 x 1.10 = \$ 1,210

1,100 x 1.102 = \$ 1,210 or

1, 000 x 1.21 = \$ 1,210

• Thus,

Future Value = PV x (1+ Interest rate)number years

Abbreviations worth?

• PV = Current/earliest lump sum amount

• FV = Ending/latest lump sum amount

• I = Interest rate earned or paid

• N = number of years/compounding periods

• FVIF = future value interest factor = (1+I)N

• FV = PV (1+I) worth?n

Example:

Invest \$500 for 4 years at 8 percent rate of return, how much will you have at the end of the fourth year?

Solution worth?

Using Formula & Table

• FV = PV (1 + I )n

• FV = PV (FVIF i, n)

• FV = \$500 (1 + .08)4

= 500 (1.360)

FV = \$ 680

With Calculator

\$500 PV

4 n

8 I

FV = \$680

If you are 20 years old and today invest \$1000 dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

Solution 7%, what will your \$1,000 be worth when you are 65 years old?

• What is the future value of \$1000 today if invested for 45 years at 7% annual interest rate?

• PV = \$1,000

• i = 7 (the I/YR key)

• N = 45

• Solve for FV FV = \$ 21,002

• Only a few mistakes are common when computing time value of money problems on an HP 10B calculator.

• Before starting a problem, make sure to check for the following:

• How many payments is your calculator set on. To check, press shift (the yellow key), then C ALL (Input on the older HP calculator).

• If a number other than what is needed appears, the number of payments may be changed by pressing the correct number of payments, then shift then PMT

• Check to see whether your calculator is in the “begin” mode. This means that payments are assumed to be made at the beginning of the time period rather than at the end of the time period, which is typically when payments are considered. If begin appears on your screen when it is not needed, press shift then BEG/END to change back to the end of the time period.

• ALWAYS clear the machine by pressing SHIFT then C ALL. Never presume the bottom left “C” button clears everything. It doesn’t.

• When using more than one compounding period per year (as in monthly payments on a 5-year loan), press the number of years, then SHIFT then N. (eg., 5 SHIFT N after having the number of payments set on 12 per year - - 12 SHIFT PMT)

• To change the number of decimal places shown to say 6 places, press SHIFT, DISP (=) 6

If you wait until you are 35 years old and invest \$1000 dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

Solution dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• \$7,612

• 1000 PV

• 7 I

• 30 N

• FV = 7,612.25

Hint: dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• Any of these variables may be computed just as easily as FV, such as a PV amount, an interest rate, or the number of years/payments, etc.

Present Value Factors dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• The reciprocal of the Future Value Factors

• PVIF = present value interest factor = 1/(1+I)N

Present Value Interest Factors dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

Present Value Example dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

You will need \$8,000 in 5 years to make a down payment on a house. How much would you need to put aside today to achieve your goal if you are earning 6% on your money?

Solution dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• \$8,000 FV

• 5 N

• 6 I

• PV = \$5,978 , i.e., is needed today to have the \$8,000 in five years.

Problem dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• If you invest \$10,000 at 6% annual interest, how long will it take your money to double?

Solution dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• PV \$10,000

• FV 20,000

• I 6

• N 12 years (11.9 years)

Rule of 72 dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• Any two numbers when multiplied together give you 72, will indicate the annual interest rate or the length of time until a sum doubles. For example,

• 2 x 36 = 72 3 x 24 = 72

• 4 x 18 = 72 6 x 12 = 72…..

• Thus, at 2% it takes 36 years for a sum to double. Likewise, at 36%, it takes 2 years for a sum to double.

• Eg., in the previous example, 6 x 12 = 72

Annuities dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• Now, let’s consider making an investment or payment more than just one time.

• Multiple payment situations are generically referred to as annuities.

• Payments may be made annually (once a year) or more frequently

• If payments are made more than once a year, be sure the calculator knows the payment frequency by pressing the number of payments per year, then SHIFT then PMT

Practice Problem dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

If you are 25 years old and invest \$1000 dollars each year at 7%, what will your investments be worth when you are 65 years old?

If you waited until you were 35 to start making those payments, how much would you have at age 65?

Solutions dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• Starting at age 25

\$1000 PMT

7 I

40 N

FV \$199,635

• Starting at age 35

\$1000 PMT

7 I

30 N

FV \$94,461

Car Payments dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• You want to borrow \$15,000 for a new car and make monthly payments for 2 years. If the bank will lend you the money for 8%, how much will your monthly payments be?

• Hint: Solve for PMT rather than PV

• Must set calculator on 12 payments per year

(press 12 shift pmt)

Solution to Car Payments dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• \$15,000 PV

• 8 I

• 2 shift N (will assume 24 pmts)

PMT ?

Car Loan Alternatives dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• What would your monthly payments be if you were charged 10% interest?

• \$692.17

• What would your monthly payments pay if you borrowed the money for 3 years at 8%?

• \$470.04

Mortgages dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• If you were to borrow \$100,000 for a house, consider the following alternatives:

• 15 years at 7.5 %

• 30 years at 8%

Mortgage Solutions dollars at 7%, what will your \$1,000 be worth when you are 65 years old?

• 15-year note

• 100,000 PV

• 7.5 I

• 15 shift N (@12 pmts per year)

• PMT 927.01

• 30-year note

• \$100,000 PV

• 8.0% I

• 30 shift N

• @12 pmts per year

• PMT \$733.76

How much more would you pay for the house over the life of the loan if you chose the 30-year note rather than the 15-year note?

Solution: 15 vs. 30-year notes the loan if you chose the 30-year note rather than the 15-year note?

15-year note

PMT \$ 927.01

TOTAL PAID:

(PMT x 12 x 15)

= \$ 166,862

30-year note

PMT \$733.76

TOTAL PAID:

= \$ 264,154

Difference: \$97,688

Amortization the loan if you chose the 30-year note rather than the 15-year note?

• The depleting or repaying of borrowed funds

• Term also used to mean the “using up of an asset”

• May be used to determine the balance of a loan at any time

Amortization Example the loan if you chose the 30-year note rather than the 15-year note?

• On the 15 and 30-year mortgage examples, what would the ending balances be at the end of the 1st year of each loan?

• HINT: Solve for the payment, then press shift AMORT (FV) then =. You will then see the time period for which the amortization will be given (eg., period 1-12 for the first year when there are monthly payments). Then press = to get the amount of interest paid during the first year; press = again to get the amount of principal paid, then = again to get the ending balance after the first year)

Amortization Answer the loan if you chose the 30-year note rather than the 15-year note?

15- year loan

1st year’s payments:

(\$11,124.15)

Interest \$7372.79

Principle \$3,751.36

Balance \$ 96,248.64

30-year loan

1st year’s payments:

(\$8,805.17)

Interest \$ 7,969.80

Principle \$ 835.37

Balance \$ 99,164.63

Ordinary Annuity the loan if you chose the 30-year note rather than the 15-year note?vs. Annuity Due

• When payments are made on a regular (say, annual) basis into an investment, the timing of the payments is important.

• If an amount is paid each year into a fund earning interest, the present or future value of that investment fund is determined by whether the payment is made at the beginning or the end of each year.

Ordinary Annuity the loan if you chose the 30-year note rather than the 15-year note?vs. Annuity Due (cont.)

• In a typical situation (ordinary annuity), the PV or FV is computed assuming the payments are all made at the end of each period.

• 3 Questions:

Ordinary vs. Annuity Due the loan if you chose the 30-year note rather than the 15-year note?Examples

• If payments of \$1000 are made each year for 10 years at 12%, how much will be accumulated at the end of the 10th year?

• How much would be accumulated if the payments were made at the beginning of each year?

• How much would you pay today for an annuity that paid you \$1000 a year for 10 years if interest rates were 12%? (assume payments at end of period)

Annuity Solutions the loan if you chose the 30-year note rather than the 15-year note?

Ordinary annuity

\$1000 pmt (1/year)

10 n

12 I

FV \$17,548.74

PV 5,650.22

Annuity Due

Turn on Begin (shift BEG/END)

\$1000 PMT

10 n

12 I

FV \$19,654.58

PV 6,328.25

### Practice Problems the loan if you chose the 30-year note rather than the 15-year note?

• It is your 18 cash in wedding gifts. If they place this money in a mutual fund earning 11%, how much will they have on their first anniversary? Their 10th birthday and you have just won a lottery worth \$250,000. However, you may not receive any funds until you are 21. If your windfall earns 8% between now and your 21st birthday, how much will you receive on you 21st birthday?

. accumulated in his pension plan and would like to withdraw it in equal annual dollar amounts so that he has withdrawn it all by age 85. How much should he withdraw each year until age 85 assuming 7% interest?

• You plan to make the following deposits to save money to buy a car in five years. At 9% interest, find the value of your deposits at the end of the 5th years:

• You deposit \$100 at the end of the 1st year

• You deposit \$200 at the end of the next 2 years

• You deposit \$500 at the end of the 4th year

• You deposit \$1000 at the end of the 5th year

Capital Budgeting Problem accumulated in his pension plan and would like to withdraw it in equal annual dollar amounts so that he has withdrawn it all by age 85. How much should he withdraw each year until age 85 assuming 7% interest?

• A new robot for your factory will cost you \$45,000 but will save you variable/manual labor costs of \$14,000 per year for 10 years. What is the present value of the investment if you must pay 8.5% for money to buy the robot?

• Suppose Olivia deposits \$10,500 into a 403B plan at the end of each of the next 25 years, what will her investment be worth in 25 years if her deposits earn 9% each year?

• What would this investment be worth at the end of the 25th year if she makes the deposits at the beginning of the year instead?

Applicable Links \$500 per month for 10 years, what rate of return are you earning on your money?

• On-line calculators

• Mutual Funds and Misc. Investments

• Stock Market

• Money rates

• Mortgage and Real Estate

• Economic Data

• Insurance Quotes

• Tax Services

On-line Calculators \$500 per month for 10 years, what rate of return are you earning on your money?

• www.techmtg.com/calc/mortgage.htm

• www.financenter.com

• www.investorguide.com

• http://pathfinder.com/

• www.calcbuilder.com

• www.401kafe.com/tools/calc.html

• http://quote.bloomberg.com/

• www.banking.yahoo.com/calculators.html

Mutual Funds and \$500 per month for 10 years, what rate of return are you earning on your money?Miscellaneous Investments

• www.brill.com

• www.closed-endfunds.com

• www.fabian.com

• www.findafund.com

• www.fundspot.com

• www.indexfundsonline.com

• www.investmentdiscovery.com

• www.morningstar.com

• www.fundz.com

• www.bondsonline.com

• www.publicdebt.treas.gov

Stock Market \$500 per month for 10 years, what rate of return are you earning on your money?

• www.411stocks.com

• www.financialweb.com

• www.investorguide.com

• www.money.net

• www.quote.com

• www.investingstocks.com

• www.quote.yahoo.com

• www.prospectusonline.com

• www.quotecentral.com

Money Rates \$500 per month for 10 years, what rate of return are you earning on your money?

• www.bankrate.com

• www.banx.com

• www.onmoney.com

• http://finance.yahoo.com

• www.bog.frb.fed.us/releases/H15

• http://www.bankrate.com/brm/default.asp

• http://bankcd.com/

• http://www.money-rates.com/

• http://www.rate.net/

Mortgage and Real Estate \$500 per month for 10 years, what rate of return are you earning on your money?

• www.microsurf.com

• www.realestate.com

• www.tnrealtor.com

• www.netquote.com

• www.loan.yahoo.com

• http://www.mortgage101.com

• http://www.homepath.com

• http://www.homemortgageguide.com

• http://www.mortgageexpert.org

Economic Data \$500 per month for 10 years, what rate of return are you earning on your money?

• www.bea.doc.gov

• www.frbchi.org

• www.fedstats.gov/key

• www.huduser.org

• http://www.mortgagemart.com/armindex.html

Insurance Quotes \$500 per month for 10 years, what rate of return are you earning on your money?

• www.insweb.com

• www.quotesmith.com

• www.quicken.com

• www.insurance.yahoo.com

• www.quickquote.com

• www.netquote.com

Tax Services \$500 per month for 10 years, what rate of return are you earning on your money?

• www.moneycentral.com

• www.irs.gov

• www.taxresources.com