3. You are saving money from working, and are planning to invest it to get the best return. Let us suppose that starting today, you save 1,000 dollars per month. You know of a unique investment plan that operates on continously compounding interest with an impressive monthly rate of 5%, meaning that if you put P dollars in, and you withdraw from it k months later, you will get back Pe0.05k dollars. However, due to financial restrictions and tax laws, you can only invest in this plan once, and you can only withdraw from the plan once. Since saving money is hard, you will stop saving after investing to pursue some hobbies and vacations. You have a friend who is willing to offer you a loan of an additional 2,000 dollars to add to this plan when you put in money, on the condition that you will repay him at 3% monthy interest once you withdraw the money, so if you withdraw after s months you must pay him back 2, 000(1.03)* dollars. Let t represent when (in months, starting from now) you invest in the plan, using money from yourself and your friend, and let s represent how many months you leave the money in the plan before withdrawing it, paying off your loan, and keeping the remainder. (a) Let f(t, s) be the amount of money you end up keeping after withdrawing from the invest- ment plan and paying off the loan. Provide f(t, s).
3. You are saving money from working, and are planning to invest it to get the best return. Let us suppose that starting today, you save 1,000 dollars per month. You know of a unique investment plan that operates on continously compounding interest with an impressive monthly rate of 5%, meaning that if you put P dollars in, and you withdraw from it k months later, you will get back Pe0.05k dollars. However, due to financial restrictions and tax laws, you can only invest in this plan once, and you can only withdraw from the plan once. Since saving money is hard, you will stop saving after investing to pursue some hobbies and vacations. You have a friend who is willing to offer you a loan of an additional 2,000 dollars to add to this plan when you put in money, on the condition that you will repay him at 3% monthy interest once you withdraw the money, so if you withdraw after s months you must pay him back 2, 000(1.03)* dollars. Let t represent when (in months, starting from now) you invest in the plan, using money from yourself and your friend, and let s represent how many months you leave the money in the plan before withdrawing it, paying off your loan, and keeping the remainder. (a) Let f(t, s) be the amount of money you end up keeping after withdrawing from the invest- ment plan and paying off the loan. Provide f(t, s).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:3.
You are saving money from working, and are planning to invest it to get
the best return. Let us suppose that starting today, you save 1,000 dollars per month. You
know of a unique investment plan that operates on continously compounding interest with an
impressive monthly rate of 5%, meaning that if you put P dollars in, and you withdraw from
it k months later, you will get back Pe0.05k dollars. However, due to financial restrictions and
tax laws, you can only invest in this plan once, and you can only withdraw from the plan once.
Since saving money is hard, you will stop saving after investing to pursue some hobbies and
vacations.
You have a friend who is willing to offer you a loan of an additional 2,000 dollars to add to
this plan when you put in money, on the condition that you will repay him at 3% monthy
interest once you withdraw the money, so if you withdraw after s months you must pay him
back 2,000(1.03)* dollars. Let t represent when (in months, starting from now) you invest in
the plan, using money from yourself and your friend, and let s represent how many months
you leave the money in the plan before withdrawing it, paying off your loan, and keeping the
remainder.
(a) Let f(t, s) be the amount of money you end up keeping after withdrawing from the invest-
ment plan and paying off the loan. Provide f(t, s).
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