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A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+)". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) = Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.

A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+)". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) = Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.

Advanced Engineering Mathematics
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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• Rewrite this limit as an indeterminate quotient and use Bernoulli's Rule to evaluate the limit. (Hint when taking derivatives: r and t are not involved in the limit with respect to n, so you can treat them like constants.) • There are just a couple more steps here. What was the actual limit we started with? What was the goal of this exercise? How do we finish? • Tell me about your process here, was this interesting? What just happened? What did you learn?
Transcribed Image Text:• Rewrite this limit as an indeterminate quotient and use Bernoulli's Rule to evaluate the limit. (Hint when taking derivatives: r and t are not involved in the limit with respect to n, so you can treat them like constants.) • There are just a couple more steps here. What was the actual limit we started with? What was the goal of this exercise? How do we finish? • Tell me about your process here, was this interesting? What just happened? What did you learn?
A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ )". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.
Transcribed Image Text:A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ )". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.
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