Understanding Money Management - Engineering Economics

7/30/2019 Understanding Money Management - Engineering Economics

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Applied Software Project Management

Engineering Economics

Understanding Money Management

http://www.stellman-greene.com 1


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Road Map

Market Interest Rates

Calculating Effective Interest Rates Based onPayment Periods

Equivalence Calculations with Effective Interest

Rates Debt Management

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The market interest: the interest rate quoted by thefinancial market, i.e. banks and financial institutions.

Interest rate: to consider any anticipated changes in

earning power as well as

purchasing power in the economy

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Pay the minimum, pay for years Making minimum payments on your credit cards can cost

you a bundle over a lot of years. Here's what wouldhappen if you paid the minimum-or more-every month on

a $2.705 card balance, with a 18.38% interest rate

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Payment Rate How Long To Pay off Debt Interest Paid

2% 27 years, 2 months 11,047

4% 08 years, 5 months 2,707

8% 02 years, 1 months 594


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Nominal Interest Rates

Financial institution uses a unit of time other than a year-for example, a month or a quarter-when calculatinginterest payments.

Institution usually quotes the interest rate on an annual

basis. For example, "18% compounded monthly." This statement means simply that each month the bank

will charge 1.5% interest (12 months per year X 1.5%per month = 18% per year) on the unpaid balance.

18% is the nominal interest rate orannual percentagerate (APR) and that the compounding frequency ismonthly (12 times per year).

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Annual Effective Yields

APR commonly used by financial institutions and isfamiliar to many customers, not explain precisely theamount of interest that will accumulate in a year.

To explain the true effect of more frequent compounding

on annual interest amounts, the term effective interestrate, commonlyknown as annual effective yield, orannual percentage yield(APY)

Annual effective yield (oreffective annual interestrate): rate truly represents the interest earned in a year

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For example, to calculate a total interest paid for a credit carddebt of $1,000 paying an interest 1.5% monthly.

P = $1,000, i = 1.5%, and N = 12

F = P(1 + i)N = $1,000(1 + 0.015)12 = $1,195.62

Total interest paid 195.62 hay 19.56% > 18% The Annual Effective Yield

M = 1, ia = i

7

1)Mr(1ai

M


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8

Nominal

RateAnnual Semi Annual Quarterly Monthly Daily

4% 4.00% 4.04% 4.06% Nhm 3 4.08%

5% 5.00%

6% 6.00%

7% 7.00%

8% 8.00% 8.16% 8.24%

9% 9.00%

10% 10.00%11% 11.00%

12% 12.00% 12.36% 12.55% 12.68% 12.74%


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Nominal

RateAnnual Semi Annual Quarterly Monthly Daily

4% 4.00% 4.04% 4.06% 4.07% 4.08%

5% 5.00%

6% 6.00%

7% 7.00%

8% 8.00%

9% 9.00%

10% 10.00%11% 11.00%

12% 12.00% 12.36% 12.55% 12.68% 12.74%


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Determine a Compound Period

Given: r = 2.23%, ia = 2.5%, find M

0.025 = (1 + 0.0223/M)M

1

1.025 = (1 + 0.0223/M)M

By trial and error, we find that M = 365, which indicatesdaily compounding

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1)Mr(1ai

M


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Road Map


Calculating Effective Interest Rates Based onPayment Periods



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Discrete Compounding

If cash flow transactions occurquarterly, but interest iscompounded monthly, to calculate the effective interestrate on a quarterly basis:

i = (1 + r/M)C - 1 or

i = (1 + r/CK)C

- 1

Where:

M = the number of interest periods per year,

C = the number of interest periods per payment period, and

K = the number of payment periods per year.Note that M = CK

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Effective Rate per Payment Period

Suppose that you make quarterly deposits into a savingsaccount that earns 8% interest compounded monthly.Compute the effective interest rate per quarter.

Given: r = 8%.

C = 3 interest periods per quarter,K = 4 quarterly paymentsper year, and

M = 12 interest periods per year.

Find: i

i= (1+8%/12)3 -1 = 2.013% per quarter

The annual effective interest rate

ia = (1 + 0.02013)4 = 8.24%

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Effective Rate per Payment Period

Suppose that you make quarterly deposits into a savingsaccount that earns 8% interest compoundedsemiannually. Compute the effective interest rate perquarter.

Given: r = 8%.C = 1/2 interest periods per quarter,

K = 4 quarterly paymentsper year, and

M = 2 interest periods per year.

Find: i

i= (1+8%/2)1/2 -1 = 1.98% per quarter

The annual effective interest rate

ia = (1 + 0.0198)4

= % 14

A li d S f P j M


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Continuous Compounding

To be competitive on the financial market, or to enticepotential depositors, some financial institutions offermore frequent compounding.

As the number of compounding periods (M) becomes

very large, the interest rate per compounding period(r/M) becomes very small. As M approaches infinity andr/M approaches zero. we approximate the situation ofcontinuous compounding

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1ei

1)CKr(1limi

1])CKr

[(1limi

r/k

C

CK

C

CK

A li d S ft P j t M t


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CaIcuIating an Effective Interest Rate

Find the effective interest rate per quarter at a nominal rateof 8% compounded (a) weekly. (b) daily, and (c)continuously.

Given: r = 8%, K = 4 payments per year. Find: i per quarter.

a) WeeklyC = M/K = 52/4 = 13

ia = (1 + r/CK)C1 = (1 + 8%/52)131 =

b) Daily

C = M/K = 365/4 = 91.25ia = (1 + r/CK)C 1 = (1 + 8%/365)91.25 1 =

c) Continuously

i = er/k-1 = e8%/4 - 1 =

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Road Map

Market Interest Rates Calculating Effective Interest Rates Based on

Payment Periods



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E i l C l l i i h


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Applied Software Project ManagementEquivalence Calculations withEffective Interest Rates

When calculating equivalent values, we need to identifyboth the interest period and the payment period.

If the time interval for compounding is different from thetime interval for cash transaction (or payment), we needto find the effective interest ratethat covers the paymentperiod

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Applied Soft are Project Management


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Calculating Auto Loan Payments

Dealers' newspaper advertisements:8.5% Annual Percentage Rate!

48-month financing on all Mustangs in stock.

60 cars to choose from

ALL READY FOR DELIVERY!Prices starting as low as $21,599

You just add sales tax and 1 % for dealer's freight.

We will pay the tag, title, and license

Add 4% sales tax = $863.96

Add 1% dealer's freight = $215.99

Total purchase price = $22,678.95

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You can afford to make a down payment of $2,678.95,so the net amount to be financed is $20,000.

a) What would the monthly payment be?

b) After the 25th payment, you want to pay off the

remaining loan in a lump sum amount. What is therequired amount of this lump sum?

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a) What would the monthly payment be?The advertisement does not specify a compounding period,

but in automobile financing, the interest and the paymentperiods are almost always monthly. Thus, the 8.5% APRmeans 8.5% compounded monthly

Given: P = $20,000, r = 8.5% per year, K = 12 paymentsper year, N = 48 months, M = 12 interest periods/year.

Find: A

i = 8.5%/12 = 0.7083%

A = P(A/P,i,N) = 20,000(A/P, 0.7083%,48)

A = 492.97

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]1Ni)(1

Ni)i(1P[A



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b) After the 25th payment, you want to pay off theremaining loan in a lump sum amount. What is therequired amount of this lump sum?

Calculating the equivalent worth of the remaining 23payments at the end of the 25th month, with the timescale shifted by 25 months:

Given:A = $492.97, i = 0.7083% per month, and N = 23months,

Find: Remaining balance after 25 months (B25

)

B25 = A(P/A,i,N) = 492.97(P/A,0.7083%,23)

B25 = 10,428.96

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Compounding Occurs at a Different Rate


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Applied Software Project ManagementCompounding Occurs at a Different Ratethan That at Which Payments Are Made

Procedure for dealing with compounding periods and

payment periods that cannot be compared is as follows:1. Identify the number of compounding periods per year

(M), the number of payment periods per year (K). andthe number of interest periods per payment period (C)

2. Compute the effective interest rate per payment period: For discrete compounding, compute

i = ( 1 + r /M)C - 1

For continuous compounding, compute

i = er/K

- 13. Find the total number of payment periods:

N = K X (number of years).

4. Use i and N in the appropriate formulas

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Compounding Occurs More


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Applied Software Project ManagementCompounding Occurs MoreFrequently than Payments Are Made

1. Identify the parameter values for M, K, and C. where M = 12 compounding periods per year,

K = four payment periods per year, and

C = three interest periods per payment period.

2. To compute effective interest: i = ( 1 + r /M)C -1 = (1 + 0.12/12)3 1

i = 3.030% per quarter

3. Find the total number of payment periods, N, where N = K (number of years) = 4 x 3 = 12 quarters.

4. Use i and N in the appropriate equivalence formulas:F = A(F/A, i, N) = 1000(F/A,3.030%,12)

F = 14,216.24

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N)A(F/A,i,]i

1Ni)(1A[F



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Road Map

Market Interest Rates Calculating Effective Interest Rates Based on

Payment Periods



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Borrowing with Credit Cards

Consumer's perspective: does not have to wait for apaycheck to reach the bank before making a purchase.

Most credit cards operate as revolving credit, i.e.

a line of borrowing that you can tap into at will

pay back as quickly or slowly as you want as long asyou pay the minimum required each month.

Four things affect card-based credit costs: annual fees,finance charges, the grace period, and the method of

calculating interest Three different ways to compute interest charges:

Adjusted Balance, Average Daily Balance, PreviousBalance

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Borrowing with Credit Cards

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Method Description Example of the Interest You Owe, Given aBeginning Balance of $3,000 at 18%

Adjusted Balance

The bank subtracts the amount of

your payment from the beginning

balance and charges you interest on

the remainder. This method costs you

the least.

With a $1,000 payment, your new balance

will be $2,000. You pay 1.5% interest for

the month on this new balance. which

comes out to (1.5%) ($2.000) = $30.

Average Daily

Balance

The bank charges you Interest on the

average of the amount you owe each

day during the period. So the larger

the payment you make, the lower the

interest you pay.

With a $1.000 payment on the 15th day,

your balance reduced to $2,000. Thereforethe interest on your average daily balance

for the month will be(l.5%)($3,000 +$2,000)/2 = $37.50.

Previous Balance

The bank does not subtract anypayments you make from your

previous balance. You pay interest on

the total amount you owe at the

beginning of the period. This method

costs you the most.

The annual interest rate is 18%compounded monthly. Regardless of your

payment size, the bank will charge 1.5%

on your beginning balance of $3.000.

Therefore, your interest for the month is

(1.5%)($3,000) = $45



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Paying Off Cards Saves a Bundle

Suppose that you owe $2,000 on a credit card thatcharges 18% APR, and you make either the minimum10% payment or $20, whichever is larger, every month.

How long will it take to pay off debt? Assume that thebank uses the adjusted-balance method to calculateyour interest.

Given:APR = 18% (or 1.5% per month). beginningbalance = $2.000, and monthly payment = 10% ofoutstanding balance or $20, whichever is larger.

Find: Number of months to pay off the loan, assumingthat no new purchases are made during this paymentperiod. (open excel file)

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Commercial Loans Calculating


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Applied Software Project ManagementCommercial Loans CalculatingPrincipal and Interest Payments

One of the most important applications of compoundinterest involves loans: paid off in installments over time.

Repaid in equal periodic amounts (e.g., weekly, monthly,quarterly, or annually): amortized loan.

Examples: automobile loans, loans for appliances. homemortgage loans, and most business debts

Most commercial loans: interest compounded monthly.

Two factors determine what borrowing will cost you: the

finance charge and the length of the loan. The cheapest loan is not necessarily the loan with the

lowest payments, or even the loan with the lowest interestrate.

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Commercial Loans Calculating


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Applied Software Project ManagementCommercial Loans CalculatingPrincipal and Interest Payments

Instead, you have to look at the total cost of borrowing.which depends on the interest rate, fees, and the term(i.e., the length of time it takes you to repay the loan).

While you probably cannot influence the rate and fees.you may be able to arrange for a shorter term

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Using Excel to Determine a Loan's


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Applied Software Project ManagementUsing Excel to Determine a Loan sBalance, Principal, and lnterest

Suppose you secure a home improvement loan in theamount of $5,000 from a local bank. The loan officergives you the following loan terms:

Contract amount = $5,000;

Contract period = 24 months; Annual percentage rate = 12%

Monthly installment = $235.37

Given: P = $5,000, A = $235.37 per month, r = 12% per

pear, M = 12 compounding periods per year, and N = 24months.

Find: Bn, and In, for n = 1 to 24.

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Using Excel to Determine a Loan's


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pp ed So a e ojec a age eUsing Excel to Determine a Loan sBalance, Principal, and lnterest

We can easily see how the bank calculated the monthlypayment of $235.37235.37(P/A, 1, 24) = 235.57 * 21.2431 = 5,000

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pp j g

Comparing Different Financing Options

Decision to pay cash, take out a loan, or sign a lease (acar) depends on a number of personal as well aseconomic factors.

1. Have enough money to buy: purchase in cash

lose the opportunity to earn interest on the amount you spend

2. Debt financing: own the vehicle at the end of your financing term

Paying the interest will drive up the real cost

3. Leasing: length of lease agreement, monthly payments,the yearly mileage allowance tailored to driving needs

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Buying a Car: Paying in Cash versus


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pp j gBuying a Car: Paying in Cash versusTaking a Loan

Option A: Purchase the vehicle at the normal price of$26,200, and pay for the vehicle over 36 months withequal monthly payments at 1.9% APR financing.

Option B: Purchase the vehicle at a discounted price of$24,048 to be paid immediately. The funds that would beused to purchase the vehicle are presently earning 5%annual interest compounded monthly

Which option is more economically sound?

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Buying a Car: Paying in Cash versus


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pp j gBuying a Car: Paying in Cash versusTaking a Loan

Option A:

With the 1.9% interest, your monthly payments will be

A = 26,200(A/P,1.9%/12,36) = 749.29

PA = 749.29(P/A, 5%/12, 36) = 25,000

Option B:PB = 24,048

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pp j g

Tutorial

Do end chapter problems: 3.3, 3.10, 3.14, 3.15, 3.18, 3.20, 3.34, 3.37, 3.40, 3.42, 3.43,

3.50, 3.61

Documents

Understanding Money Management - Engineering Economics