# Zero Interest Credit Card Offers by cny68055

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```									FV Example 1: \$100 Initial Deposit Only
6% Annual Interest, 3 years, Compounds Semi-Annually.

Compounds:                        Semi-Annually
Yearly Rate
Years
Payments
Initial Deposit (PV)
Type
Future Value

FV Example 2: \$5000 Initial Deposit & \$200 per month Deposits
4% Annual Interest, 18 Years, Compounded Monthly

Compounds:                        Monthly
Yearly Rate
Years
Monthly Payments
Initial Deposit (PV)
Type
Future Value

FV Example 3: \$500 Yearly Payments
4% Annual Interest, 10 Years, Beg. Of Period

Compounds:                        Yearly
Yearly Rate
Years
Payments
Initial Deposit (PV)
Type
Future Value
You are opening an account with \$100. The account compounds
semi-annually. At 6% yearly interest, what will you have in 3 years?

You wish to open a account for you newborn’s college in 18 years.
You plan on making an initial deposit of \$5,000 and making monthly
deposits of \$200.
The account compounds monthly with a yearly rate of 4%.

How much will you have in 18 Years?

You are depositing \$5,000 into an account yearly for the next 10
years at 4% annual interest. Interest is compounded yearly at the
beginning of the period.

What is the Future Value?
=Effect(Nominal Rate,Number of Compounding Periods Per Year)

Effective Rate Example 1:        Comparing Different Loan Rates
We are looking for a credit card company that offers the best rate and have found three we wish to compare.
The first has a nominal rate of 17% and compounds monthly, the second has a rate of 17.5% and compounds
semi-annually (twice a year), and the third has a rate of 18% and compounds quarterly. Which one has the best

Nominal Rate                                    Periods Per Year Effective Rate
17.0%                 12
17.5%                  2
18.0%                  4

Effective Rate Example 2:      FV with Yearly Payments, Compounding Monthly
We are making yearly payments of \$1000 for 5 years into an account which compounds monthly
nominal interest rate is 6%. The payments are made at the end of each year (regular annuity).

The number of payments per year must equal the number of compounding periods per year.
Because Payments are made yearly, we need an equivalent rate which compounds yearly (i.e. the effective

Example 2: Payments & Compounding Periods Differ (5 Year Loan)
Annual Rate:
Number of Times Compounded per year:
Life of Loan:
Type:

Rate Equivalent Using Effect()

Future Value:
three we wish to compare.
e of 17.5% and compounds
terly. Which one has the best

monthly. The annual
ar annuity).

s per year.
s yearly (i.e. the effective
=Effect(Nominal Rate,Number of Compounding Periods Per Year)
=Nominal(Effective Rate,Number of Compounding Periods Per Year)

We are making semi-yearly payments of \$1000 into an account for 3 years. The account compounds
annual nominal interest rate is 4%. The payments are made at the end of each period (regular annuity). Find the
Future Value.

The number of payments we are making per year must equal the number of compounding
Step 1: First, we will find the Effective yearly rate equilavent of an account which compounds monthly.
Step 2: Now that we have the effective yearly rate, we use nominal() to convert it into the nominal rate for an account

Payments & Compounding Periods Differ (5 Year Loan)
Annual Rate:
Number of Times Compounded per year:
Life of Loan:
Payments (Semi-Yearly):
Type:

Effective Yrly Rate for an account compounding Monthly:
Nominal Yrly Rate for an account compounding Semi-Annually:
Future Value:
The account compounds monthly. The
ach period (regular annuity). Find the

f compounding periods per year.
which compounds monthly.
vert it into the nominal rate for an account
You are loaning an associate \$1,000. For repayment options, the suggest the scenarios below. The
going market rate is 4% compounded monthly. Which option should you take? Assume risk is the
same for all three options.

OPTION A:       Will pay you \$1,200 after 1 year.
OPTION B:       Will pay you \$1,400 at the end of 2 years.
OPTION C:       Will pay you \$100 per month for 12 months then \$150.

Scenario                               Option A                    Option B           Option C
Yearly Rate:
Years:
Payments:
Future Value:
Type:

Present Value:
Bond Cash Flow Discounting Example – PV()
We have purchased a 3 year bond with a face value of \$1,000 for \$961.15. Its coupon rate is 6% resulting in yearly
payments of \$60 (face value x coupon rate). The market is currently paying about 5% for investments of equal risk. What
is the Bond's Present Value?

=PV(Rate,#periods,CouponPayment,FaceValue)

Bond Cash Flow Discounting Example - PV()
Face Value:
Years to Maturity:
Coupon Rate:
Present Value (Purchase Price):
Discount Rate Used for Valuation:
Yearly Coupon Payments:

Present Value: (Includes Coupon Payments + Face Value)
s 6% resulting in yearly
vestments of equal risk. What
=PMT(Rate,#ofPeriods,PV,FV,Type)

PMT Example 1: Loan Payments                          You are planning to buy a new car. You are takin
Rate:                                                 5 year loan of \$20,000 to help you pay for it and
Years:                                                borrowing at an interest rate of 6%. What will t
Present Value
Future Value
Type

Monthly Payments:

PMT Example 2: Retirement Goal Using Effective Rate
Nominal Rate:                                                  You would like to have \$1,000,000 in yo
Effective Rate:                                                account by the time you retire. You ha
Years:                                                         retirement and you have found a CD ac
5.5% annual interest. You plan on mak
Present Value
payments into an account which comp
Future Value
How much do you have to deposit each

Yearly Payments:                                               Effect(Nominal Rate,Compounding Per
ing to buy a new car. You are taking out a
an interest rate of 6%. What will the

would like to have \$1,000,000 in your savings
unt by the time you retire. You have 30 years until
ement and you have found a CD account which pays
annual interest. You plan on making yearly
ments into an account which compounds monthly.
much do you have to deposit each year to reach

ct(Nominal Rate,Compounding Periods)
=NPER(Rate,Payments,PV,FV,Type)
You are planning on making montlhly deposits of \$100 into a savings
account which compounds monthly with a yearly rate of 4%. How
many years will it take you to have \$25,000?
What will the date be? (From the current date?)

Rate
Payments
Present Value
Future Value
Type

Number of Periods:
Number of Years:

Today's Date:
Target Date:
Rate(#periods,Payments,PresentValue,FutureValue,Type,Guess)
Rate Example 1: Return on your Investment: Single Payment
Present Value:
Periods (In Years):
Payments:
Future Value:
Yearly Rate if Compounded Yearly:
Monthly Rate if Compounded Monthly:
Yearly Rate if Compounded Monthly:

Rate Example 2: Return on your Inventment - Multiple Payments   You are investing in
Purchase Price (PV)                                             \$50 at the end of every 6 mon
Compounding Periods:                                            payments). At the end of the
Payments:                                                       payment of \$209,18.
Future Value:
Rate Per Period:                                                What rate are you getting for
Rate Per Year:                                                  What rate are you getting per
5 Years ago you purchased a 1969 Ford Falcon for \$5,000 and spent
\$1000 fixing it up the day you purchased it. You sold it today for
\$10,000.

What return did you get on your investment ?
Find the Yearly Rate if Compounded Yearly.
Find the Montly Rate if compounded Monthly.
Find the Yearly Rate if Compounded Monthly.

You are investing in an annuity that requires you to deposit
\$50 at the end of every 6 months for 2 years (i.e. total of 4
payments). At the end of the 2 years you will receive a
payment of \$209,18.

What rate are you getting for each period?
What rate are you getting per year?
NPV() - FINDING PRESENT VALUE OF AN ANNUITY WHEN CASH FLOWS VARY
The PV requires that the cash flows all be of an equal amount (i.e. an annuity). This section shows how to use Excel’s NPV()
series of cash flows are evenly spaced but of varying amounts.

=NPV(Rate,Range of Cash Flows)
Rate:           This is the rate of interest over one period.
Range of Cash Flows:              These must be equally spaced apart in time but may vary in amount.

The cash flows must be at the END of the period.
The cash flows must be in the order they occur over time.

The sign is important. When using NPV(), cash outflows should always be negative and inflows positive.

NPV() Example 1:Initial Investment is Today – Cash Flows Vary
You are considering an investment opportunity that will cost you \$3,000 today and pay the following amounts at the end
\$700, \$900, and \$850. The going interest rate of investments of similar risk is 6%. Should you make the investment?

NPV Example 1 - Investment Today                                                 NPV Example 2 - Investment in One Year
Annual Rate:                                                                     Annual Rate:

Year                     Amount                                                  Year
1                                                                                1
2                                                                                2
3                                                                                3
4                                                                                4
5                                                                                5
6
Present Value:
Net Present Value:                                                               Net Present Value:
FLOWS VARY
n shows how to use Excel’s NPV() function to determine the Present Value when a

n amount.

nflows positive.

he following amounts at the end of each year for the following 5 years: \$500, \$600,
d you make the investment?

ple 2 - Investment in One Year

Amount
Internal Rate of Return: =IRR(Values,Guess)

It is the interest rate received for an investment consisting of payments and income what occur at regular
periods. More technically, the Internal Rate of return of a series of cash flows is the discount rate which sets
the sum of the present value of these cash flows to zero. When comparing multiple investments, the higher
the rate the better and negative rates are always bad.

IRR Example 1
- Cash flows must occur at regular period
Year                           Amount                                                  - The amount of the cash flows do
0                                                           for an annuity.
- IRR uses the order of values to interpre
1
enter your payment and income values i
2
- The initial flow is the investment and m
3                                                           should be positive. If in one of your year
4                                                           cannot use Excel's IRR function. A negati
5                                                           and Excel only displays a single value for

Internal Rate of Return:                                                               Note that IRR assumes cash generated d
the rate calculated by IRR. This can over
generate a lot of cash over the life of the
at regular
te which sets
s, the higher

must occur at regular periods.
nt of the cash flows do not have to be identical as they would be

he order of values to interpret the order of cash flows. Be sure to
payment and income values in the sequence they occur.
flow is the investment and must be negative. Subsequent flows
ositive. If in one of your years you have a negative cash flow, you
Excel's IRR function. A negative cash flow produces and second IRR
nly displays a single value for IRR. Use MIRR instead.

R assumes cash generated during the investment is reinvested at
culated by IRR. This can overstate IRR for investments which
ot of cash over the life of the investment.
Modified Internal Rate of Return: =MIRR(Values,FinanceRate,ReinventRate)

IRR assumes that the rate you finance your investment is the same as the rate you reinent your
profits. Further, it cannot have any negative cash flows after the initial inventment. MIRR
addresses both of these issues. You can use MIRR() if you have any future negative cash flows.

MIRR Example 2: Single Investment
Investment
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7

Finance Rate:
Reinvest Rate:

MIRR
Bond Cash Flow Discounting Example – PV()
In this example, we wish to see the profit made if our cash flows were discounted. We will use Excel’s
PV() function to find their present value. Our bond is a 3 year bond with a 6% coupon rate paid annually,
and a \$1,000 face value which we purchased for \$961.25. The market is currently paying about 5% for
investments of equal risk. Find the present value of your cash inflows.

=PV(Rate,#periods,CouponPayment,FaceValue)

Bond Cash Flow Discounting Example - PV()
Face Value:
Years to Maturity:
Coupon Rate:
Present Value (Purchase Price):
Discount Rate Used for Valuation:
Yearly Coupon Payments:

Present Value:
(Includes Coupon Payments + Face Value)
Bond Cash Flow Discounting Example – NPV()
This is the same example as on the "Bonds_PV" tab, this time we will use NPV() instead. Our bond
is a 3 year bond with a 6% coupon rate paid annually, and a \$1,000 face value which we purchased
for \$961.15. The market is currently paying about 5% for investments of equal risk. Find your net
discounted profit.

=NPV(Rate,CashFlows)

Bond Cash Flow Discounting Example - NPV()
Face Value:
Years to Maturity:
Coupon Rate:
Present Value (Purchase Price):
Discount Rate Used for Valuation:
Y1 Coupon Payment
Y2 Coupon Payment
Y3 Coupon Payment + Face Value:

Net Present Value:
Bond Example – Yield to Maturity using Rate()
You have purchased a bond with a face value of \$1,000 and coupon rate of 6% at a discount of
96-08. It is a 3 year bond and pays semi-annually. What is the Yield to Maturity?

Rate(#periods,Payments,PurchasePrice,FaceValue,Type,Guess)

Bond Example: Yield to Maturity Using Rate() On Date
Face Value:
Coupon Rate:
Years to Maturity:
Payments Per Year:
Purchase Rate (96-08):
Purchase Price:
Yield to Maturity:
Bond Example – Yield to Maturity using IRR()
You have purchased a bond with a face value of \$1,000 and coupon rate of 6% at a discount of
96-08. It is a 3 year bond and pays semi-annually. What is its Internal Rate of Return?

IRR(Range)

Bond Example: Yield to Maturity Using IRR() - On Date
Investment:
Payment 1
Payment 2
Payment 3
Payment 4
Payment 5
Payment 6 + Face Value
Semi-Annual IRR:
Yearly IRR:
Yield(Settlement,Maturity,CouponRate,PR,Redemption,Frequency,Basis)

Settlement              Maturity       Coupon Rate     PR            Redemption         Frequency
This is the date you    This is the    This is the     The Market    Amount paid by     The number
take ownership of the   maturity       annual coupon   Price as a    issuer as a non-   of coupon
bond. Typically 3       date written   rate written    non-decimal   decimal percent    payments per
days after the trade.   on the bond.   on the bond.    percent of    of Face Value.     year.
Face Value.

Bond Example - YTM for off Coupon Date Sales

Quoted Bond Price:                                                              Bond Example YTM using Yield()
Face Value:                                                                     Coupon Date
Maturity Date:                                                                  On March 3, 2009 you purchased a bo
Purchase Date (Settlement Date):                                                \$1,000 and a coupon rate of 8% paid s
Previous Coupon Date:                                                           last coupon date was on 12/15/2008 a
Rate:                                                                           you not including accrued interest was
matures on 12/15/2019. What is the Y
Payment Frequency:

YTM Using Yield():
ency,Basis)

Frequency       Basis
The number      Day count
of coupon       basis to use.
payments per    (See chart
below.)

Example YTM using Yield() – Bond Not Purchased on

rch 3, 2009 you purchased a bond with a face value of
and a coupon rate of 8% paid semi-annually. The bond’s
upon date was on 12/15/2008 and the price quoted to
t including accrued interest was \$961.25. The bond
es on 12/15/2019. What is the Yield to Maturity?
Bond Valuation Model - Price()
Required Annual Rate:
=Price(SettlementDate
Face Value
Redemption as % of Par             Settlement
Annual Coupon Rate                 Date
Payment Frequency                  This is the
date you
Issue Date
purchased the
Maturity Date                      bond.
Settlement Date
First Interest Payment Date
Day Count Basis                   Basis
You can calculate the numbe
Price as % of Par:                number of days in the year by
Clean Price in Dollars:           is some use 365/frequency w

Accrued Interest
Dirty Price:

=Accrint(

Calc Method (Optional)
This becomes importan
interest from the issue d
Price(SettlementDate,MaturityDate,Rate,RequiredYield,Redemption,Frequency,Basis)

Settlement         Maturity           Rate                Required Yield        Redemption             Frequency             Basis
Date               Date               This is the         This is the           This is the            # of coupon           Method used to
This is the        This is the        annual              minimum               bond’s payoff          payments per          calculate the
date you           date the bond      interest rate       desired rate of       per \$100 of            year.                 number of days
purchased the      is due.            written on the      return you are        face value.                                  between
bond.                                 bond.               willing to
accept.

Basis
You can calculate the number of days between coupon payments by dividing the                0 (or omitted): US (NASD) 30/360
number of days in the year by the number of compounding periods per year. The issue         1Actual/actual
is some use 365/frequency while others might use 360/frequency. The numbers to the          2Actual/360
3Actual/365
4European 30/360

=Accrint(IssueDate,FirstInterestDate,SettlementDate,Par,Frequency,Basis,CalcMethod

Issue Date          First Interest     Settlement           Par                Frequency                Basis
Date the bond       Date               Date                 Bond’s face        # of coupon              See
was issued.         Date of the        Date you             value.             payments per             above.
first interest     purchased the
payment.

Calc Method (Optional)
This becomes important when the settlement date is after the first interest date and affects how interest is calculated. Type
interest from the issue date to settlement date and type 0 returns interest from the 1st payment date to settlement date.
Type 1     Accrued Interest

Issue                                                     1st Interest                                               Settlement
Payment
Type 0     Accrued Interest
)

Basis
Method used to
calculate the
number of days
between

S (NASD) 30/360

CalcMethod)

Basis        Calc Method
See          See below.
above.

est is calculated. Type 1 returns
to settlement date.

Settlement

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