# Pure Expectations Theory and Spot Rate

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Introduction to Finance

Week 3 Numerical Exercises:

S. No. Problem

1 If the one-year spot rate is 5% (R1) (APR) and Two-year spot rate is 5.5% (R2) (APR) calculate the one-year rate one-year (Forward rate)(FR1) from today using pure expectations theory.

2 Given the following table:

Type of Security Interest Rate

5-Year Treasury Note 5%

5-Year Corporate Bond (High quality) 6%

5-Year Corporate Bond (Low quality) 8%

Calculate the default risk premium (DRP) on the Corporate bonds.

3

Present Value Years Interest Rate Future Value

$570 15 10%

$8,922 9 18%

$61,133 3 12%

$219,850 10 4%

Given the above data, calculate the future value in each case. (Using the formula and also a financial calculator)

4

Future Value Years Interest Rate Present Value

$349 10 6%

$5,227 20 2%

$48,950 12 12%

$612,511 7 10%

Given the above data, calculate the present value in each case. (Using the formula and also a financial calculator).

5 Given the following data, solve for the interest rate in each case. (Use a financial calculator)

Present Value Years Future Value Interest Rate

$475 4 $615

$7,350 7 $18,350

$27,175 11 $65,000

$93,412 19 $200,000

6 You expect your newly born child to attend college in 18 years. You have $12,000 to set aside for that purpose. You also expect that the total cost of college education to be $100,000 by that time.

Calculate the interest rate at which you have to invest today to achieve your goal.

7 How long does it take to double your money at 9 % interest rate?

8 How long does it take to triple your money at 9 % interest rate?

9 Great Lakes Inc. has an unfunded pension liability of $300 million that must be paid in 18 years. The financial analyst wants to discount this liability back to present for valuation purposes.

The appropriate discount rate is 8%.

What is the present value of this liability?

10 Highlight Inc. is considering an investment project with the following cash flows:

YEAR Cash Flow

1 $300

2 $400

3 $600

4 $900

If the discount rate is 10% , calculate the present value of these cash flows

What will be the present value if the discount rate is changed to 15%

11 Solarlight Inc is considering a project with the following cash flows :

YEAR Cash Flow

1 $800

2 $700

3 $600

4 $500

Calculate the future value of these cash flows in year 4., if the interest rate is 12%

What will be the present value if the interest rate is changed to 16%?

12 Newsys Inc. will generate $30,000 per year for the next five years from a new database system. The system requires an investment of 120,000 today. If the opportunity cost of funds is 6%, is the system worth installing?

13 An investment pays $2,000 per year for 10 years. The payments occur at the end of each year The required rate of return in 12%.

Calculate the value of the investment today.

What will be its value if the payments occurred at the beginning of each year?

14 If Mr. Hobbit deposits $2,000 at the end of each year for the next 10 years at an interest rate of 12% per year, how much will be have accumulated? How much will he have accumulated if he deposited the amounts at the beginning of each year?

15 Find the present value of a perpetuity that pays $2,000 per year and the interest rate is 10%

16 Show, using an example, that the present value of an annuity is the difference between the present value of two perpetuities, one starting one year from today and the other starting N+1 years from today.

17 Given the following data, calculate the effective annual rate (EAR) in each case

Sated rate (Nominal APR) Frequency of Compounding Effective rate (EAR)

10% Monthly

12% Quarterly

8% Daily(use 365 days)

18 Given the following data, calculate the stated (Nominal) annual rate (APR) in each case

Sated rate (Nominal APR) Frequency of Compounding Effective rate (EAR)

Monthly 12%

Quarterly 6 %

Daily (use 365 days) 15%

19 Big Bank Corp. wants to earn an effective interest rate of 9% (EAR) on its consumer loans. It uses monthly compounding on consumer loans. What should be the stated (Nominal) rate (APR) on these loans?

20 Calculate the future value of $1,000 in 10 years assuming an interest rate of 12% (APR) compounded quarterly.

Also calculate the effective rate (EAR) on the investment.

21 You want to buy a new sports coupe and need $30,000 loan and the finance company affiliated with the dealership is offering 6.9% APR loan and the loan calls for 60 monthly payments. What will be your monthly payments and also the effective interest rate on the loan?

22 Mr. Wise is retiring in 25 years. He would like to accumulate $1,000,000 for his retirement fund by then. He plans make equal monthly payments to achieve his goal. If the rate of return on the retirement fund is 12%, what will his monthly payments be?

23 Mr. Wise makes payments (as per problem 33) for the first ten years and stops making payments afterwards due personal problems.

How much would he have accumulated at the time of retirement assuming that the accumulated amount still earns interest at the stated rate on a monthly basis?

24 Prepare an amortization schedule for a three year loan of $10,000. The interest rate is 9% per year, and the loan calls for equal annual payments.

How much interest is paid over the life of the loan? (use a financial calculator)

(Also, develop the amortization schedule using Excel spread sheet)

25 Mr. Spend has accumulated credit card loans of $15,000 and is finding it difficult to make payments. His local bank has offered him a consolidation loan to payoff all the credit card loans. The loan calls for monthly payments for 10 years and has a nominal interest rate of 5.99% (APR). What will Mr. Spend's monthly payments be if he takes the loan?

Credit Card Loan Amount Monthly Payment

Visa 1 $3,000 $90

Visa 2 $5,000 $120

Visa 3 $6,000 $150

Master Card 1 $1,000 $20

26 Mr. Carter is planning to buy a home and he expects to borrow $200,000 for that purpose. Currently 15-year mortgage loans are quoted at 5% (APR). He expects to make monthly payments towards the loan.

Calculate his monthly payments.

What will be the outstanding amount on the loan after making payments for 5 years?

#### Solution Summary

The pure expectations theory and spot rate are determined.