Pesonal finance 6th madura chapter 03 applying time value concepts

All Rights Reserved3.1 Describe the importance of the time value of money 3.2 Calculate the future value of a dollar amount that you save today 3.3 Calculate the present value of a dolla

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SIXTH EDITION

Chapter 3

Applying Time Value

Concepts

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3.1 Describe the importance of the time value of money

3.2 Calculate the future value of a dollar amount that you save today

3.3 Calculate the present value of a dollar amount that will be received in the future 3.4 Calculate the future value of an annuity

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3.5 Calculate the present value of an annuity

3.6 Explain how time value can be used to estimate savings 3.7 Explain how time value fits within your financial plan

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– Annuity: a series of equal cash flow payments that are received or paid at equal intervals in time

– An example would be a monthly deposit of $50 into your savings account

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know:

– The interest rate to be earned on the deposit

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a factor multiplied by today’s savings to determine how the savings will accumulate over time

– Future value table shows various interest rates (i) and time periods (n)

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$5,000 now and earn an annual return of 4 percent

– The present value of money (PV) is the amount invested, or $5,000

– Find the interest rate of 4 percent and a time period of five years on the table

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years, your money will be worth:

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– As the number of years increases, the FVIF increases

– What if you invested your $5,000 for 20 years instead of 5 years? Assuming the interest rate is still 4%:

$5,000 x 2.191 = $10,955

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– The higher the interest rate, the more your money will grow

– What if you invested your $5,000 at an interest rate of 9% instead of 4%? Assuming a period of

20 years:

$5,000 x 5.604 = $28,020

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 Not only do you pay interest on your debt, you also pay interest on the interest on your debt

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– Some people believe that it is to their advantage to postpone payment of debt as long as possible

 More enjoyable to spend than to pay!

– They fail to recognize how debt can accumulate over a long-term period

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amount at some future time

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– The amount of money to be received in the future

– The interest rate to be earned on the deposit

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– Present value interest factor (PVIF):

a factor multiplied by a future value to determine the present value of that amount

– Notice that PVIF is lower as the number of years increases and as the interest rate increases

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today You believe you can achieve a return from your investment of 7 percent

annually What is the dollar amount that you need to invest today to achieve your goal?

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period

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savings level (annuity) to determine how the savings will accumulate over time

– i is the periodic interest rate

– n is the number of payments in the annuity

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year for the next 20 years As soon as you receive the payments, you will invest them

at your bank at an interest rate of 7 percent annually How much will be in your account

at the end of 20 years, assuming you do not make any withdrawals?

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you would have:

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the future value of your savings

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of the annuity and adding them up

financial calculator

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savings level (annuity) to determine the present value of the annuity

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$82,000 at the end of every year for the next 25 years Now, a financial firm offers you

a lump sum of $700,000 in return for these payments If you can invest your money at

an annual interest rate of 9 percent, should you accept the offer?

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the stream of $82,000 payments is:

$82,000 x 9.823 = $805,486

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– Provides motivation for regular saving

– Helps set specific goals when saving for a large purchase

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– Money can grow substantially over time when you invest periodically and earn interest

– May be more motivated to save because you can see the reward of your effort

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– How much should I attempt to accumulate in savings for a future point in time?

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concepts to help her devise a savings plan that fits her budget

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EXHIBIT 3.2 How Time Value of Money Decisions Fit Within Stephanie Spratt’s Financial Plan

GOALS FOR A SAVINGS PLAN

1 Calculate how much savings I will accumulate by various future points in time.

2 Determine how much I need to save each year to ensure a comfortable living upon retirement.

ANALYSIS

Present Situation:

Expected Savings per Year = $5,000

Expected Annual Rate of Return = 6% or 7%

Estimated Amount of Savings to Be Accumulated:

Savings Accumulated over:

Assume Annual Return = 6%

Assume Annual Return = 7%

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Annual Savings Needed to Achieve a Specific Savings Goal:

Savings Goal = $80,000 in 10 years, $200,000 in 20 years, $600,000 in 30 years

Expected Annual Rate of Return = 6% or 7%

$80,000 in 10 years $6,069 $5,790

$200,000 in 20 years 5,437 4,879

$600,000 in 30 years 7,589 6,352

To achieve a savings goal of $80,000 in 10 years, I would need to save $6,069 per year (assuming an annual return of 6% on my money) To achieve a goal of $200,000 in 20 years,

I would need to save $5,437 per year (assuming a 6% annual return).

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DECISIONS

Decision on My Savings Goal in the Future:

If I can save $5,000 a year, I should accumulate $28,185 in 5 years and $65,905 in 10 years These estimates are based on an assumed annual return of 6% If my annual return is higher, I should accumulate even more than that The estimated savings for longer time periods are much higher

A comparison of the third column with the second column in the table shows how much more savings I could accumulate if I can earn an annual return of 7% instead of 6%.

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Decision on My Savings Goal per Year:

Although my initial plan was to develop a budget for saving about $5,000 a year, I will try to save more so that I can achieve my savings goals I will use a minimum savings goal of $5,000, but will try to save about $6,000 per year.

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