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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_forwardPresent value is the amount of money that must be invested now at a given rate of interest to produce a given future value. For a 1-year investment, the present value can be calculated using Present value = Future value 1 + r , where r is the yearly interest rate expressed as a decimal. (Thus, if the yearly interest rate is 8%, then 1 + r = 1.08.) If an investment yielding a yearly interest rate of 13% is available, what is the present value of an investment that will be worth $4000 at the end of 1 year? That is, how much must be invested today at 13% in order for the investment to have a value of $4000 at the end of a year? (Round your answer to two decimal places.)arrow_forwardThe amount that should be set aside is $ (Round up to the nearest dollar.)arrow_forward
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- A loan of $4800 is to be repaid with quarterly payments for 4 years at 11.8% interest compounded quarterly. Calculate the quarterly payment. Identify the appropriate formula needed to calculate the quarterly payment. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) O A. P= F (1+1)^' OB. F= = (1+i)^ -1 with P = $ n= O c. R=- •R, with F = $ i 1-(1+i)n •P, with P = $ and i= % n= n= and i= and i= % %arrow_forwardA fast growth share has the first dividend (t=1) of $3.16. Dividends are then expected to grow at a rate of 5 percent p.a. for a further 3 years. It then will settle to a constant-growth rate of 2.6 percent. . If the required rate of return is 13 percent, what is the current price of the share? (to the nearest cent) O a. $27.38 O b. $32.19 c. $30.38 O d. $69.53arrow_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_forward
- Your 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_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_forwardI do not know how to set this question up, how would I do it to get the correct answers?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage