1405 Words6 Pages

5-42 Integrated Case

Time Value of Money Analysis. You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money analysis covering the following questions: a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2; (2) an ordinary annuity of $100 per year for 3 years; and (3) an uneven cash flow stream of -$50, $100, $75 and $50 at the end of Years 0 through 3.

(1)

100

0

1

2

100

0

1

2

(2)

I%I%

I%I%

(3)

100

50

75

0

1

2

3

-50

100

50

75

0

1

2

3

-50

b. 1. What’s the future value of $100 after 3 years if it earns 10%, annual compounding?

FV = PV (1 + I)N = $100 (1.10)3 = $133.10 2. What’s the*…show more content…*

Why? * The future value will be larger if we compound an initial amount more often than annually. For example, you deposit $100 in a bank that pays a 10% annual interest rate but credits interest each 6 months. Therefore, in the second 6-month period, you earn interest on your original $100 plus interest on the interest earned during the first 6 months. 14. Define (a) the stated (or quoted or nominal) rate, (b) the periodic rate, and (c) the effective annual rate (EAR or EFF%).

(a) The stated rate is the contracted or quoted interest rate and is also referred to as the annual percentage rate (APR).

(b) The periodic rate is the annual percentage rate divided by the number of periods per year.

(c) The effective annual rate is the annual rate of interest actually being earned, as opposed to the quoted rate. 15. What is the EAR corresponding to a nominal rate of 10% compounded semiannually? Compounded quarterly? Compounded daily? * Compounded Semiannually:

EAR = [1+ 0.10/2]2 – 1 = 0.1025 = 10.25% * Compounded Quarterly:

EAR = [1+ 0.10/4]4 – 1 = 0.1038 = 10.38% * Compounded Daily:

EAR = [1+ 0.10/365]365 – 1 = 0.1052 = 10.52% 16. What is the future value of $100 after 3 years under 10% semiannual compounding? Quarterly compounding? * Semiannual Compounding:

IPER = I / M = 10% / 2 = 5%

Number of Periods = NM = (3)(2) = 6

FV = $100 (1.05)6 =

Time Value of Money Analysis. You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money analysis covering the following questions: a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2; (2) an ordinary annuity of $100 per year for 3 years; and (3) an uneven cash flow stream of -$50, $100, $75 and $50 at the end of Years 0 through 3.

(1)

100

0

1

2

100

0

1

2

(2)

I%I%

I%I%

(3)

100

50

75

0

1

2

3

-50

100

50

75

0

1

2

3

-50

b. 1. What’s the future value of $100 after 3 years if it earns 10%, annual compounding?

FV = PV (1 + I)N = $100 (1.10)3 = $133.10 2. What’s the

Why? * The future value will be larger if we compound an initial amount more often than annually. For example, you deposit $100 in a bank that pays a 10% annual interest rate but credits interest each 6 months. Therefore, in the second 6-month period, you earn interest on your original $100 plus interest on the interest earned during the first 6 months. 14. Define (a) the stated (or quoted or nominal) rate, (b) the periodic rate, and (c) the effective annual rate (EAR or EFF%).

(a) The stated rate is the contracted or quoted interest rate and is also referred to as the annual percentage rate (APR).

(b) The periodic rate is the annual percentage rate divided by the number of periods per year.

(c) The effective annual rate is the annual rate of interest actually being earned, as opposed to the quoted rate. 15. What is the EAR corresponding to a nominal rate of 10% compounded semiannually? Compounded quarterly? Compounded daily? * Compounded Semiannually:

EAR = [1+ 0.10/2]2 – 1 = 0.1025 = 10.25% * Compounded Quarterly:

EAR = [1+ 0.10/4]4 – 1 = 0.1038 = 10.38% * Compounded Daily:

EAR = [1+ 0.10/365]365 – 1 = 0.1052 = 10.52% 16. What is the future value of $100 after 3 years under 10% semiannual compounding? Quarterly compounding? * Semiannual Compounding:

IPER = I / M = 10% / 2 = 5%

Number of Periods = NM = (3)(2) = 6

FV = $100 (1.05)6 =

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