7.4. Suppose that an annuity pays $10,000 per year for 10 years, with payments made continuously. We will compute the present value of this income stream, assuming an annual interest rate of year 7.4. Suppose that an annuity pays $10,000 per year for 10 years, with payments made continuously. We will compute the present value of this income stream, assuming an annual interest rate of 4% (r = 0.04/year). (a) Determine upper and lower bounds for the present value of the first year's payments. Bear in mind that a dollar paid immediately is worth $1, but a dollar paid at the end of the year is worth e" dollars. (b) Repeat part (a) for years 2 through 10. 7.6. Exercises 211 (c) Add up the pieces for years 1 through 10 to get upper and lower bounds for the present value of the entire annuity. (d) Average the upper and lower bounds from part (c) to get a good estimate for the present value of the annuity. This is (approximately) what an in- surance company would charge you for this annuity.
7.4. Suppose that an annuity pays $10,000 per year for 10 years, with payments made continuously. We will compute the present value of this income stream, assuming an annual interest rate of year 7.4. Suppose that an annuity pays $10,000 per year for 10 years, with payments made continuously. We will compute the present value of this income stream, assuming an annual interest rate of 4% (r = 0.04/year). (a) Determine upper and lower bounds for the present value of the first year's payments. Bear in mind that a dollar paid immediately is worth $1, but a dollar paid at the end of the year is worth e" dollars. (b) Repeat part (a) for years 2 through 10. 7.6. Exercises 211 (c) Add up the pieces for years 1 through 10 to get upper and lower bounds for the present value of the entire annuity. (d) Average the upper and lower bounds from part (c) to get a good estimate for the present value of the annuity. This is (approximately) what an in- surance company would charge you for this annuity.
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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Transcribed Image Text:7.4. Suppose that an annuity pays $10,000 per year for
10 years, with payments made continuously. We will
compute the present value of this income stream,
assuming an annual interest rate of year
7.4.
Suppose that an annuity pays $10,000 per year for 10 years, with payments
made continuously. We will compute the present value of this income stream,
assuming an annual interest rate of 4% (r = 0.04/year).
(a) Determine upper and lower bounds for the present value of the first year's
payments. Bear in mind that a dollar paid immediately is worth $1, but a
dollar paid at the end of the year is worth e" dollars.
(b) Repeat part (a) for years 2 through 10.
7.6. Exercises
211
(c) Add up the pieces for years 1 through 10 to get upper and lower bounds
for the present value of the entire annuity.
(d) Average the upper and lower bounds from part (c) to get a good estimate
for the present value of the annuity. This is (approximately) what an in-
surance company would charge you for this annuity.
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