Sarah must to pay $5000 to Jason one year from today and $9000 to Robert two yea

ID: 3141597 • Letter: S

Question

Sarah must to pay $5000 to Jason one year from today and $9000 to Robert two years from today. To match the obligations, Sarah plans to purchase bonds today. The following bonds are available for purchase today:

* One-year zero-coupon bonds with 7% yield

* Two-year zero coupon bonds with 6.5% annual yield

* Two-year 4% par-value bond with annual coupons and 6% annual yield

Sarah purchases the bonds so that the redemption amount of the two-year zero-coupon bond is 4 times the redemption amount of the two-year coupon bond. Find the purchase prices for each of these bonds if Sarah uses the bonds to exactly match the obligations.

One-year zero-coupon bond: $__________

Two-year zero-coupon bond: $_________

Two-year coupon bond: $_____________

Explanation / Answer

Ans-

FV = PV (1+i )n Using the (yx) Key

1.06 yx 4 =, you will see the factors is: 1.2625

If you multiply the $500 by the factor you get the following answer:

$500 x 1.2625 = $631.25

You can check it with your calculator: 500 +/- PV, 4 n, 6 i, FV = $632.2385

Using TVM Tables

Assume a client wants to know the Future Value of an investment of $500 in an investment with an interest rate of 6%, which they will sell in 4 years.

Future Value Table

Interest Rate

1.0000

1.0100

1.0200

1.0300

1.0400

1.0600

1.0800

1.1000

1.0000

1.0201

1.0404

1.0609

1.0816

1.1236

1.1664

1.2100

1.0000

1.0303

1.0612

1.0927

1.1249

1.1910

1.2597

1.3310

1.0000

1.0406

1.0824

1.1255

1.1699

1.2625

1.3605

1.4641

1.0000

1.0510

1.1041

1.1593

1.2167

1.3382

1.4693

1.6105

First remember to use the correct table. There are different tables for different types of problems.

Here if you cross-reference the 6% and the 4 periods, you will see the factors is: 1.2625

If you multiply the $500 by the factor you get the following answer, $500 x 1.2625 = $631.25

Setting Up Your HP-10BII Calculator

Setting the number of Decimals (to 4 places)

SHIFT DISP 4

Setting the Compounding Periods Per Year To 1

1 SHIFT P/YR

Setting Your Calculator to END Mode (for an Ordinary Annuity)

SHIFT BEG/END

Clearing the Memory

SHIFT CLEAR ALL

Using Your Financial Calculator

Only think in terms of Number of Periods (Not years or quarters)

You only need to take a small number of different factors into consideration from each TVM Problem, and plug them into your calculator:

PV FV PMT

n (Remember, this is not necessarily the number of years)

i (Also, this is not necessarily the annual rate)

Begin

Cash Flow Keys Include (note that these keys are not used with the others and vice versa):

CFj Nj

NPV IRR

For both problems you will need the:

+/-, This key tells the calculator that money is going INTO the problem. The easy way to remember this is to: Always use the +/- key when you are taking money out of your pocket and putting it into the problem!

Serial Interest Rate: (1 + Growth Rate ÷ 1 + Inflation Rate) – 1 x 100 =

Things to REMBER!!! When Using Your Financial Calculator

FV Single Sum

Today, Bill purchased a large ring for $50,000. He expects it to increase in value at a rate of 15% compound Annually for the next 5 years. How much will his ring be worth at the end of the 5th year?

Clear Your Calculator

50,000 +/- PV

15 i

5 n

$100,567.86

Future Value of a Single Sum

$1,000 is invested at 8% compounded annually for 3 years. What will its value be?

Clear Your Calculator

1,000 +/- PV

8 I

3 n

$1,259.71

Present Value of a Single Sum

Client will receive $1,000 in 3 years. What will it be worth today if the opportunity cost is 8%.

Clear Your Calculator

1,000 FV

8 i

3 n

-793.83

Future Value

Today Bob Jones purchased an investment grade gold coin for $50,000. He expects the coin to increase in value at a rate of 12% compounded annually for the next 5 years. How much will the coin be worth at the end of the fifth year if his expectations are correct?

a. $89,792.82

b. $6691 1.28

c. $88,117.08

d. $89,542.38

e. None of the above

50,000 +/- PV

5 n

12 i

0 PMT

FV = $88,117.08

Future Value

A client invested $10,000 in an interest-bearing promissory note earning an 11% annual rate of interest compounded monthly. How much will the note be worth at the end of 7 years assuming all interest is reinvested at the 11% rate?

a. $13,788.43

b. $20,762.60

c. $21,048.52

d. $21,522.04

e. None of the above

10,000 +/- PV

11 ¸ 12 = 0.91666 i

7 x 12 = 84 n

0 PMT

FV = $21,522.04

FV = PV (1+i )n Using the (yx) Key

1.06 yx 4 =, you will see the factors is: 1.2625

If you multiply the $500 by the factor you get the following answer:

$500 x 1.2625 = $631.25

You can check it with your calculator: 500 +/- PV, 4 n, 6 i, FV = $632.2385

Using TVM Tables

Assume a client wants to know the Future Value of an investment of $500 in an investment with an interest rate of 6%, which they will sell in 4 years.

Future Value Table

Interest Rate

1.0000

1.0100

1.0200

1.0300

1.0400

1.0600

1.0800

1.1000

1.0000

1.0201

1.0404

1.0609

1.0816

1.1236

1.1664

1.2100

1.0000

1.0303

1.0612

1.0927

1.1249

1.1910

1.2597

1.3310

1.0000

1.0406

1.0824

1.1255

1.1699

1.2625

1.3605

1.4641

1.0000

1.0510

1.1041

1.1593

1.2167

1.3382

1.4693

1.6105

First remember to use the correct table. There are different tables for different types of problems.

Here if you cross-reference the 6% and the 4 periods, you will see the factors is: 1.2625

If you multiply the $500 by the factor you get the following answer, $500 x 1.2625 = $631.25

Setting Up Your HP-10BII Calculator

Setting the number of Decimals (to 4 places)

SHIFT DISP 4

Setting the Compounding Periods Per Year To 1

1 SHIFT P/YR

Setting Your Calculator to END Mode (for an Ordinary Annuity)

SHIFT BEG/END

Clearing the Memory

SHIFT CLEAR ALL

Using Your Financial Calculator

Only think in terms of Number of Periods (Not years or quarters)

You only need to take a small number of different factors into consideration from each TVM Problem, and plug them into your calculator:

PV FV PMT

n (Remember, this is not necessarily the number of years)

i (Also, this is not necessarily the annual rate)

Begin

Cash Flow Keys Include (note that these keys are not used with the others and vice versa):

CFj Nj

NPV IRR

For both problems you will need the:

Serial Interest Rate: (1 + Growth Rate ÷ 1 + Inflation Rate) – 1 x 100 =

Things to REMBER!!! When Using Your Financial Calculator

FV Single Sum

Today, Bill purchased a large ring for $50,000. He expects it to increase in value at a rate of 15% compound Annually for the next 5 years. How much will his ring be worth at the end of the 5th year?

Clear Your Calculator

50,000 +/- PV

15 i

5 n

$100,567.86

Future Value of a Single Sum

$1,000 is invested at 8% compounded annually for 3 years. What will its value be?

Clear Your Calculator

1,000 +/- PV

8 I

3 n

$1,259.71

Present Value of a Single Sum

Client will receive $1,000 in 3 years. What will it be worth today if the opportunity cost is 8%.

Clear Your Calculator

1,000 FV

8 i

3 n

-793.83

Future Value

a. $89,792.82

b. $6691 1.28

c. $88,117.08

d. $89,542.38

e. None of the above

50,000 +/- PV

5 n

12 i

0 PMT

FV = $88,117.08

Future Value

a. $13,788.43

b. $20,762.60

c. $21,048.52

d. $21,522.04

e. None of the above

10,000 +/- PV

11 ¸ 12 = 0.91666 i

7 x 12 = 84 n

0 PMT

FV = $21,522.04

Future Value Table

Interest Rate

1.0000

1.0100

1.0200

1.0300

1.0400

1.0600

1.0800

1.1000

1.0000

1.0201

1.0404

1.0609

1.0816

1.1236

1.1664

1.2100

1.0000

1.0303

1.0612

1.0927

1.1249

1.1910

1.2597

1.3310

1.0000

1.0406

1.0824

1.1255

1.1699

1.2625

1.3605

1.4641

1.0000

1.0510

1.1041

1.1593

1.2167

1.3382

1.4693

1.6105

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