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Preview Activity 9.1.1. Suppose you invest money in an account that pays 5% interest compounded continuously. If you invest P dollars in the account, the amount A of money in the account after t years is given by A = Pe0.05t The variables P and t are independent of each other, so using functional notation we write A(P,t) = Pe0.05t a. Find the amount of money in the account after 7 years if you originally invest 1000 dollars. b. Evaluate A(5000, 8). Explain in words what this calculation represents. c. Now consider only the situation where the amount invested is fixed at 1000 dollars. Calculate the amount of money in the account after t years as indicated in Table 9.1.1. Round payments to the nearest penny. Table 9.1.1. Amount of money in an account with an initial investment of 1000 dollars. Duration (in years) 2 Amount (dollars) 3 4 5 6

Preview Activity 9.1.1. Suppose you invest money in an account that pays 5% interest compounded continuously. If you invest P dollars in the account, the amount A of money in the account after t years is given by A = Pe0.05t The variables P and t are independent of each other, so using functional notation we write A(P,t) = Pe0.05t a. Find the amount of money in the account after 7 years if you originally invest 1000 dollars. b. Evaluate A(5000, 8). Explain in words what this calculation represents. c. Now consider only the situation where the amount invested is fixed at 1000 dollars. Calculate the amount of money in the account after t years as indicated in Table 9.1.1. Round payments to the nearest penny. Table 9.1.1. Amount of money in an account with an initial investment of 1000 dollars. Duration (in years) 2 Amount (dollars) 3 4 5 6

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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Preview Activity 9.1.1. Suppose you invest money in an account that pays 5% interest compounded continuously. If you invest P dollars in the account, the amount A of money in the account after t years is given by Pe0.05t A - The variables P and t are independent of each other, so using functional notation we write A(P, t) = Pe0.05t a. Find the amount of money in the account after 7 years if you originally invest 1000 dollars. b. Evaluate A(5000, 8). Explain in words what this calculation represents. c. Now consider only the situation where the amount invested is fixed at 1000 dollars. Calculate the amount of money in the account after t years as indicated in Table 9.1.1. Round payments to the nearest penny. Table 9.1.1. Amount of money in an account with an initial investment of 1000 dollars. Duration (in years) 2 3 4 5 6 Amount (dollars) d. Now consider the situation where we want to know the amount of money in the account after 10 years given various initial investments. Calculate the amount of money in the account as indicated in Table 9.1.2. Round payments to the nearest penny. Table 9.1.2. Amount of money in an account after 10 years. Initial investment (dollars) 500 1000 5000 7500 10000 Amount (dollars) e. Describe as best you can the combinations of initial investments and time that result in an account containing $10,000.
Transcribed Image Text:Preview Activity 9.1.1. Suppose you invest money in an account that pays 5% interest compounded continuously. If you invest P dollars in the account, the amount A of money in the account after t years is given by Pe0.05t A - The variables P and t are independent of each other, so using functional notation we write A(P, t) = Pe0.05t a. Find the amount of money in the account after 7 years if you originally invest 1000 dollars. b. Evaluate A(5000, 8). Explain in words what this calculation represents. c. Now consider only the situation where the amount invested is fixed at 1000 dollars. Calculate the amount of money in the account after t years as indicated in Table 9.1.1. Round payments to the nearest penny. Table 9.1.1. Amount of money in an account with an initial investment of 1000 dollars. Duration (in years) 2 3 4 5 6 Amount (dollars) d. Now consider the situation where we want to know the amount of money in the account after 10 years given various initial investments. Calculate the amount of money in the account as indicated in Table 9.1.2. Round payments to the nearest penny. Table 9.1.2. Amount of money in an account after 10 years. Initial investment (dollars) 500 1000 5000 7500 10000 Amount (dollars) e. Describe as best you can the combinations of initial investments and time that result in an account containing $10,000.
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