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Loan problems The following initial value problems model the payoff of a loan. In each case, solve the initial value problem, for t ≥ 0, graph the solution, and determine the first month in which the loan balance is zero.
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Chapter 9 Solutions
Calculus: Early Transcendentals (3rd Edition)
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- An investor deposits an initial amount of money (Yo) into a bank account that offers a simple (annually compounding) interest rate (r). The bank charges a fixed annual fee (b). The bank charge is debited after the interest is accumulated. Write down a difference equation that describes how the account balance (Yt) changes over time (t), then solve the equation analytically. If the interest rate is r = 0.1(10%), the bank charge is b = 100 and the investor projects that the account balance in year t = 3 is $2,464, then the %3D initial amount of money is: Select one: Select one: O yo = $2,000 O yo = $2, 100 O yo = $2, 200 O yo = $1,900arrow_forwardPeter is contributing money to an investment account so that he can purchase a house in five years. Peter plans to contribute six payments of $3,000 a year--the first payment will be made today (t = 0), and the final payment will be made five years from now (t = 5). If he earns 11 percent in his investment account, how much money will he have in the account five years from now (at t = 5)?arrow_forwardIf $1 dollar is deposited in an account paying 27% per year compounded annually, then after t years the account will contain y = (1 + 0.27) = 1.27 dollars. (a) Use a calculator to complete the table. (b) Graph 1.27'. (a) Use a calculator to complete the table. 1 2 4 5 6 y 1.27 1.61 3.3 4.2 (Round to two decimal places as needed.) Help me solve this View an example Get more help - R D G Harrow_forward
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- I do not know how to set this question up, how would I do it to get the correct answers?arrow_forwardAn investment grows according to the formula B = 6000 x 1.0065 dollars, where t is time, measured in months. In parts (b) and (c), round your answer to the nearest whole month. (a) What was the initial balance of the investment? $ 6000 (b) How many months does it take for the balance to double? 107 months (c) How many more months does it take for the balance to double again? monthsarrow_forwardYour are the finance manager for a company that just had a great year. Last year’s income statement and this year’s expectations indicate that the company has a surplus of cash. You decide to invest $100,000 of this cash in a 5 year CD that compounds monthly. The total amount of the investment after the 5 years is given by: A(r)=100,000(1+ r/12)^60 . where r is the annual interest rate. Assuming that the interest rate is 3% (r = 0.03): 1. What is the total amount of the investment after 5 years?2. How fast is the amount growing with respect to r, in dollars per percent?arrow_forward
- Suppose that P dollars in principal is invested in an account earning 3.4% interest compounded continuously. At the end of 5 yr, the amount in the account has earned $1760.40 in interest. Part: 0 / 2 Part 1 of 2 (a) Find the original principal. Round to the nearest dollar. (Hint: Use the model A = Pert and substitute P+1760.40 for A.) The original principal was approximately 9500 X Part: 1 / 2 Part 2 of 2 (b) Using the original principal from part (a) and the model A = Pet, determine the time required for the investment to reach $11,500. Round to 1 decimal place. Using the original principal from part (a) and the model A = Pe, it will take the investment approximately yr to reach $11,500.arrow_forwardSolve asaparrow_forwardA 5-year contract provides earnings which can be modeled by the income function: c(t)=300,000+200,000tc(t)=300,000+200,000tIf the annual inflation rate is 3 %, then the present value of the contract is given by: ∫50(300,000+200,000t)e−0.03tdt∫05(300,000+200,000t)e-0.03tdtFind the present value of the contract. You may use technology to evaluate the integral and should round your final answer to two decimal places.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage