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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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Calculus: Early Transcendentals (2nd Edition)
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- The value of the account will be $ enter your response here. (Round to the nearest dollar as needed.)arrow_forwardThe sum of 1,000 is borrowed at an interest rate of 10%, elective annually. The loan must be paid in two equal installments, at the end of 1 year and after two years. How much should the installments be? Suggestion: Let x be the amount to be paid. Then the present value of receiving x dollars in (1) year plus the present value of receiving x dollars in two (2) years must equal the present value of receiving $ 1000 now.arrow_forwardIf you lend $5800 to a friend for 15 months at 4% annual simple interest, find the future value of the loan. Step 1 We want to find the future value of a loan in which you lend $5800 for 15 months at 4% annual simple interest. The future value of a loan is given by S = P + I, where P is the principal Since we are using simple interest, the interest, I, is given by I = Prt. In this problem, the principal is P = $ 5800 time is t = years. ✓ ✔ and I is the interest the interest rate as a decimal is r = C ✔ and the amount ofarrow_forward
- The simple interest on an investment is directly proportional to the amount of the investment. By investing $5800 in a municipal bond, you obtained an interest payment of $221.25 after 1 year. Find a mathematical model that gives the interest I for this municipal bond after 1 year in terms of the amount invested P. (Round your answer to three decimal places.) I= 26.215P I=221.25P I= 0.038P I= 1,283,250P I=5800Parrow_forward6. Loan payments Let N(r) be the number of $300 monthly payments required to repay an $18,000 auto loan when the interest rate is r percent. What does the equation N(6.5) = 73 say in this context?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
- A drug taken orally is absorbed into the bloodstream at the rate of te-0.5t milligrams per hour, where t is the number of hours since the drug was taken. Find the total amount of the drug absorbed (in mg) during the first 7 hours. (Round your answers to two decimal places.) mg absorbed amount absorption rate t Hours (a) Solve without using a graphing calculator. mg (b) Verify your answer to part (a) using a graphing calculator. mgarrow_forwardINSTRUCTIONS: Solve the following problems. Show a clear and organize solutions for full credits. Use 5 decimal place mantissa. 1. Find the solution of the equation f(x) = In(x+ 2) – e* using bisection method with a-0 and b-0.5. Stop when stop when Ib-al<0.0005.arrow_forwardFind the economic profit for this scenario. Principal: $2,000 Rate: 7% compounded continuously Time: 2.5 years Risk free rate: 4% annuallyarrow_forward
- 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_forward(b) Tara's aunt invests $2000 for her when she is born. The interest rate is 3.5% per year. This rate does not change as long as the money stays invested. The interest is added to the amount she has invested on her birthday each year. The value of the investment after years can be modelled by the equation A = 2000 ×(1.035)' where the A is the value of the investment. (1) How long would it take for the value of the investment to be $2250? (ii) Tara reaches her 18th birthday. Calculate how much extra the investment will be worth if she leaves the money invested for another 3 years beyond her 18th birthday. (iii) Tara is calculating 2000 x 1.035™ (1.035"-1) With reference to the investment, explain what Tara is calculating.arrow_forwardH3.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage