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PF CH3: Time Value of Money

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Silviana Falcon

on 23 October 2017

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Transcript of PF CH3: Time Value of Money

Learning Objectives
A Dollar.....
Is a dollar received today WORTH more or less than a dollar received tomorrow?....
Would you rather have your brother/sister/friend repay you $5.00 he owes you today or two years from now?
Personal Finance:
Time Value of Money

Explain the mechanics of compounding.

Calculate the future and present value.

Understand the Rule of 72

Learning Objectives

Would you rather receive $1,000 today or receive $10,000 ten years from now?
Would you rather pay for a pizza party today and have it 50 years from now?
Inflation Calculator; Bureau of Labor Statistics
is a general sustained upward movement of prices for goods and services in an economy.
As inflation rises, each dollar buys less or a smaller percentage of goods/services. If inflation rate is 2% annually, an item costing a $1 will cost $1.02 in a year.

If people accept the risk of inflation they must be compensated with interest payments on savings or on loans to cover the losses in purchasing power.
Simple Interest:
Simple Interest on $1,000 @12%
Deposit of $1,000 on Jan. 1…
$1,000 + (1,000 x .12) = $1,120 Resulting balance on Dec. 31
Compounding Interest:
Process whereby the value of an investment increases exponentially over time due to earning interest on interest previously earned
Compound Interest Quarterly on $1,000 @12%
12% ÷ 4 time periods = 3% per quarter
Deposit of $1,000 on Jan. 1…
$1,000.00 + (1,000.00 x .03) = 1,000.00 + 30.00 = $1,030.00
$1,030.00 + (1,030.00 x .03) = 1,030.00 + 30.90 = $1,060.90
$1,060.90 + (1,060.90 x .03) = 1,060.90 + 31.83 = $1,092.73
$1,092.73 + (1,092.73 x .03) = 1,092.73 + 32.78 = $1,125.51
Resulting interest yield Dec. 31...
30.00 + 30.90 + 31.83 + 32.78 = $125.51 Annual Yield

125.51/1,000 = 12.55% APY
APY = (1 + r/n)n – 1

r = stated annual interest rate
n = number of times compounded/year

Annual Percentage Yield (APY)

Compound Interest Calculator (money, time and interest rate)
Causes of Inflation?
Significant debate over specific causes. Two main theories:
1) Demand-Pull inflation: Where the demand is growing at a faster rate than the supply.
2) Cost-Push inflation: When costs of production go up, prices go up to protect profit margins.
Anticipated inflation is good.....lets people adjust
(banks vary interest rates, wage increases based on inflation (cost of living increases).
Unanticipated inflation creates havoc:
Consumers are less likely to spend
Declined on purchasing power for fixed incomes individuals/families.

Future Value.....

If one wanted to determine what amount they would like to receive one year from now in lieu of receiving $1,000 today, the individual would use the future value formula.

Example of Future Value Formula FV=pv*(1+r)n
An individual would like to determine their ending balance after one year on an account that earns .5% per month and is compounded monthly. The original balance on the account is $1000. For this example, the original balance, which can also be referred to as initial cash flow or present value, would be $1000, r would be .005(.5%), and n would be 12 (months).

Putting this into the formula, we would have: FV=$1,000 x (1+.005)12

After solving, the ending balance after 12 months would be $1061.68.

As a side note, notice that 6% (.5% x 12 months) of $1000 is $60. The additional $1.68 earned in this example is due to compounding.
The Rule of 72
(approximation) Y= 72/r
You can determine how many years it will take for a given amount to double by simply dividing the annual growth or interest rate by 72.
Growth rate: 9%/year
72/9 = 8 years for your sum to double
Before you access the website, there is a short cut:
Bankrate.com or Moneychimp.com
OR...what about if you want to know the interest rate it will take to double your money...you just run it backwards r=72/Y. if I want to double my investment in 6 years = 72/6=12%
The compound rate in the stock market over a 60 year period (1954 to 2014): 10.9%
Bottom Line of savings/compounding:
If you receive an inheritance of $10,000 and invest it at 6% for 40 years, how much would the investment grow to be?
What would happen if you invest it at 12% for 40 years?
Present Value
(of a future sum: inverse of compounding)
Suppose you have $5,000 to invest. David offers to double your money in five years. Amy offers to quadruple your money in seven years - which one will you choose? (which one would yield a better rate of return?)
You have been promised an inheritance of $500,000 in 40 years- what if you want it now......assuming a 6% discount rate- what is the present value?
Best protection is KNOWLEDGE
For money to grow: Time and interest rate
Compounding may be quarterly, monthly, daily, or even a continuous basis.

Money grows faster as the compounding period becomes shorter.

Interest earned on interest more frequently grows money faster.
Money & time
Money has a time value because it can be invested to make more money.

A dollar received in the future has lesser value than a dollar received today.

Conversely, a dollar received today is more valuable than a dollar received in the future because it can be invested to make more money.
"Money makes money. And the money that money makes makes more money." — Benjamin Franklin
Opportunity Cost

Opportunity cost, in terms of the use of money, is the benefit forfeited by using the money in a particular way.

For instance, if I spend $100 instead of depositing it in a bank that pays 5% interest, I forgo the interest by spending it instead of saving it, and if I would have saved it, then I forfeit the benefit of what I purchased.
Another Quick Way.....


David? Amy?
Y= 72/r
Y=72/5 years
Y=14.4% return will be approx. $10,000

Y=72/7 years
Y=10.28% return will be approx. $10,000 WAIT Quadrupled.
Y=20.57% return will be $20,000

Like Driving a Bugatti
Using that analogy, however imperfect it may be, we can identify several important relationships between the variables:

• The future value is always bigger than the present value.

• From any given present value (starting point), the longer you drive (N) or the faster you go (i), the bigger the future value will be.

• If you slow down (use a lower interest rate), it will take longer (larger N) to get from the present value to the future value. If you speed up (higher interest rate), you will get there faster (lower N).

• If you drive for less time (lower N), you will have to go faster (higher i) to reach the same destination (FV).

Understand the power of time and the importance of interest rate in compounding.
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