Chapter 5, Problem 41SP

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14th Edition

Eugene F. Brigham + 1 other

ISBN: 9781285867977

Textbook Problem

**TIME VALUE OF MONEY** Answer the following questions:

- a. Assuming a rate of 10% annually, find the FV of $1,000 after 5 years.
- b. What is the investment’s FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years?
- c. Find the PV of $1,000 due in 5 years if the discount rate is 10%.
- d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5 years?
- e. Suppose California’s population is 36.5 million people and its population is expected to grow by 2% annually. How long will it take for the population to double?
- f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the interest rate is 15%. What is the annuity’s FV?
- g. How will the PV and FV of the annuity in part 1 change if it is an annuity due?
- h. What will the FV and the PV be for $1,000 due in 5 years if the interest rate is 10%, semiannual compounding?
- i. What will the annual payments be for an ordinary annuity for 10 years with a PV of $1,000 if the interest rate is 8%? What will the payments be if this is an annuity due?
- j. Find the PV and the FV of an investment that pays 8% annually and makes the following end-of-year payments:

- k. Five banks offer nominal rates of 6% on deposits; but A pays interest annually; B pays semiannually; C pays quarterly; D pays monthly; and E pays daily.
- 1. What effective annual rate does each bank pay? If you deposit $5,000 in each bank today, how much will you have in each bank at the end of 1 year? 2 years?
- 2. If all of the banks are insured by the government (the FDIC) and thus are equally risky, will they be equally able to attract funds? If not (and the TVM is the only consideration), what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A?
- 3. Suppose you don’t have the $5,000 but need it at the end of 1 year. You plan to make a series of deposits—annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E—with payments beginning today. How large must the payments be to each bank?
- 4. Even if the five banks provided the same effective annual rate, would a rational investor be indifferent between the banks? Explain.

1. Suppose you borrow $15,000. The loan’s annual interest rate is 8%. and it requires four equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances.

**a.**

Summary Introduction

**To calculate:** Future value of $1,000 after 5 years at 10% annual interest rate.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

Explanation

Calculation in spreadsheet by āFVā formula,

**Table (1)**

Steps required to calculate present value by using āFVā function in excel are given,

- Select āFormulasā option from Menu Bar of Excel sheet...

**b.**

Summary Introduction

**To calculate:** Investments future value at 0%,5% and 20% rate after 0,1,2,3,4 and 5 years.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**c.**

Summary Introduction

**To calculate:** Present value due of $1,000 in 5 years at the discount rate of 10%.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**d.**

Summary Introduction

**To calculate:** Rate of return of security $1,000 and returns as $2,000 after 5 years.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**e.**

Summary Introduction

**To calculate:** Time taken by 36.5 million populations to double with annual growth rate of 2%

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**f.**

Summary Introduction

**To calculate:** Present and future value of annuity that pays $1,000 each of the next 5 years with interest rate of 15%.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**g.**

Summary Introduction

**To calculate:** Present and future value of part ‘f’ if the annuity is due.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**h.**

Summary Introduction

**To calculate:** Present and future value for $1,000, due in 5 years with 10% semiannual compounding.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**i.**

Summary Introduction

**To calculate:** Annual payments for an ordinary annuity for 10 years with PV of $1,000, interest rate 8% and payments of annuity due.

**Introduction:**

**Time Value of Money:** It is a vital concept to the investors, as it suggests them the money they are having today is worth more than the value promised in the future.

**j.**

Summary Introduction

**To calculate:** Present value and future value of an investment that pays 8% annually and makes the year end payments of $100, $200,$300.

**k.1.**

Summary Introduction

**To calculate:** Effective annual rate each bank pays and the future value of $5,000 at the end of 1 and 2 year.

**2.**

Summary Introduction

**To explain:** If banks are insured by the government and are equally risky, will they be equally able to attract funds and at what nominal rate all banks provide equal effective rate as Bank A.

**3.**

Summary Introduction

**To calculate:** Present value of amount to get $5,000 after 1 year.

**4.**

Summary Introduction

**To explain:** If all banks are providing a same effective interest rate would rational investor be indifferent between the banks.

Summary Introduction

**To prepare:** Amortization schedule to show annual payments, interest payments, principal payments, and beginning and ending loan balances.

**Amortization:**

Amotization means to write off or pay the debt over the priod of time it can be for loan or intangible assets. Its main purpose is to get cost recovery. Example of amortization is ,an automobile company that spent $20 million dollars on a design patent with a useful life of 20 years. The amortization value for that company will be $1 million each year.

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