a. What initial balance would you need to invest so that after 5 years at a continuous interest rate of 6% per year, the investment would be worth the same as the amount found in problem #1? Round answer to the nearest whole number and include correct units. b. Write an integral that represents the present value of an income stream of $100,000 per year for 5 years that is reinvested at a continuous interest rate of 6% per year. c. Evaluate this integral to find the present value of the income stream. Round answer to the nearest whole number and include units.
a. What initial balance would you need to invest so that after 5 years at a continuous interest rate of 6% per year, the investment would be worth the same as the amount found in problem #1? Round answer to the nearest whole number and include correct units. b. Write an integral that represents the present value of an income stream of $100,000 per year for 5 years that is reinvested at a continuous interest rate of 6% per year. c. Evaluate this integral to find the present value of the income stream. Round answer to the nearest whole number and include units.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In problem #1, you found the future value of an income stream of $100,000 per year over five years that was reinvested at a rate of 6% per year compounded continuously.
a. What initial balance would you need to invest so that after 5 years at a continuous interest rate of 6% per year, the investment would be worth the same as the amount found in problem #1? Round answer to the nearest whole number and include correct units.
b. Write an integral that represents the present value of an income stream of $100,000 per year for 5 years that is reinvested at a continuous interest rate of 6% per year.
c. Evaluate this integral to find the present value of the income stream. Round answer to the nearest whole number and include units.
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