Problems1. The following are exercises in future (terminal) values:a. At the end of three years, how much is an initial deposit of $100 worth, assuming acompound annual interest rate of (i) 100 percent? (ii) 10 percent? (ii) 0 percent?b. At the end of five years, how much is an initial $500 deposit followed by five year-end,annual $100 payments worth, assuming a compound annual interest rate of (i) 10 per-cent? (ii) 5 percent? (iii) 0 percent?65 t. At the end of six years, how much is an initial $500 deposit followed by five year-end,annual S100 payments worth, assuming a compound annual interest rate of (i) 10 per-cent? (ii) 5 percent? (iii) 0 percent?d. At the end of three years, how much is an initial $100 deposit worth, assuming a quar-terly compounded annual interest rate of (i) 100 percent? (ii) 10 percent?Why do your answers to Part (d) differ from those to Part (a)?At the end of 10 years, how much is a $100 initial deposit worth, assuming an annualinterest rate of 10 percent compounded (i) annually? (ii) semiannually? (iii) quarterly?(iv) continuously?

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1. The following are exercises in future (terminal) values: a. At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent?

1. The following are exercises in future (terminal) values: a. At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Concept explainers

Present Value

Present value (PV) is defined as the current or present value of all future sums of cash flow or money at a specified rate of return. This rate of return is known as the discounted rate, which is essentially the interest rate, discounted over some time. The expected cash flows are discounted at a discount rate to compute the present value. The higher the discount rate, the higher the future value (FV), but the lower the present value.

Question

Problems
1. The following are exercises in future (terminal) values:
a. At the end of three years, how much is an initial deposit of $100 worth, assuming a
compound annual interest rate of (i) 100 percent? (ii) 10 percent? (ii) 0 percent?
b. At the end of five years, how much is an initial $500 deposit followed by five year-end,
annual $100 payments worth, assuming a compound annual interest rate of (i) 10 per-
cent? (ii) 5 percent? (iii) 0 percent?
65

t. At the end of six years, how much is an initial $500 deposit followed by five year-end,
annual S100 payments worth, assuming a compound annual interest rate of (i) 10 per-
cent? (ii) 5 percent? (iii) 0 percent?
d. At the end of three years, how much is an initial $100 deposit worth, assuming a quar-
terly compounded annual interest rate of (i) 100 percent? (ii) 10 percent?
Why do your answers to Part (d) differ from those to Part (a)?
At the end of 10 years, how much is a $100 initial deposit worth, assuming an annual
interest rate of 10 percent compounded (i) annually? (ii) semiannually? (iii) quarterly?
(iv) continuously?

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2. Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semiannually. If you make 20 consecutive semiannual deposits of $500 each, with the first deposit being made today, what will your balance be at the end of Year 20? $57,900.83 $58,988.19 O $52,821.19 O $64,131.50 O $62,527.47
2. Find the present value of $500 due in the future under each of these conditions: a. 12% nominal rate, semiannual compounding, discounted back 5 years b. 12% nominal rate, quarterly compounding, discounted back 5 years c. 12% nominal rate, monthly compounding, discounted back 1 year Hint: identify the interest rate per period and the total number of periods in each scenario first. O
For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor. 1. In a future value of 1 table: Annual Rate Number of Years Invested Compounded (a) Rate of Interest a. 9% 12 Annually b. 8% 7 Quarterly C. 12% 16 Semiannually % % % (b) Number of Periods 2. In a present value of an annuity of 1 table: (Round "Rate of Interest" answers to 1 decimal place, e.g. 4.5% and other answers to O decimal places, e.g 45.) Annual Number of Years Rate Invested Number of Rents Involved Frequency of Rents (a) Rate of Interest (b) Number of Periods a. 10% 28 28 Annually b. 10% 15 30 Semiannually % % 8% 7 28 Quarterly %
Suppose the term structure of interest rates is shown below: Term Rate (EAR%) 1 year 5.00% 2 years 3 years 5 years 10 years 20 years 4.50% 4.30% 4.30% 4.25% 4.15% The present value of receiving $1000 per year with certainty at the end of the next three years is closest to:
For each of the following cases, indicate (a) what interest rate columns and (b) what number of periods you would refer to in looking up the future value factor. (1) In Table 1 (future value of 1): Number of Annual Rate Years Invested Compounded Case A 5% 5 Annually Case B 8% 6 Semiannually Case A Case B . (a) % % (2) In Table 2 (future value of an annuity of 1): Annual Rate Number of Years Invested Compounded Case A 6% 9 Annually Case B 8% 5 Semiannually Case A Case B (b) periods periods (a) (b) % periods % periods
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Suppose that the interest rate is 5 percent. Instructions: Enter your answers rounded to 2 decimal places. a. What is the future value of $100 six years from now? $ How much of the future value is total interest? $ b. By how much would total interest be greater at an interest rate of 7 percent than at an interest rate of 5 percent?
3. Use the formula for computing future value using compound interest to determine the value of an account at the end of 10 years if a principal amount of $17,000 is deposited in an account at an annual interest rate of 4% and the interest is compounded quarterly. The amount after 10 years will be $_____ (Round to the nearest cent as needed.)
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Suppose you are going to invest $11,000 per year for six years. The appropriate interest rate is 9 percent. What is the future value if the payments are made on the last day of the year? What if the payments are made on the first day of the year? a) $82,756.68; $90,204.78 b) $90,204.78; $82,756.68 c) $49,345.10; $53,786.16 d) $53,786.16; $49,345.10

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