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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 (3rd Edition)
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- London owes $7, 000 on her credit card. The bank charges an annual interest rate of 16.8%, compounded monthly. If London wants to pay off her credit card using equal monthly payments over the next 18 months, what would the monthly payment be, to the nearest dollar? Pr M 1- (1+r)-" M = the monthly payment P = the amount owed r = the interest rate per month n = the number of paymentsarrow_forwardThe value of the account will be $ enter your response here. (Round to the nearest dollar as needed.)arrow_forwardSolve for the activity no.4arrow_forward
- A certain manufacturer of Blu-ray players will make x thousand units available in the market per week when the unit price is p = 100(0.9x + 0.51/ 1 + x) dollars. What is the producers' surplus if the selling price is set at $370/unit? (Round your answer to the nearest dollar.) $_________arrow_forward[A: 3] 2. What is the simple interest rate per annum if you incurred interest of $60 over 8 months if you borrowed $2500 from Credit Mart? [A: 3] 3. Zane earned $100 when placing $400 in his bank account after a certain number of years at an interest rate of 2.5% per year, earning simple interest. Determine [A: 3] how long his money was invested for.arrow_forwardA universal life policy is issued to a life aged 45. Death benefit is 10,000 and the policyholder pays an annual premium of 200 at the beginning of each year. Expense charges are 30% of first year premium and 5% of renewal premiums. Interest credited is 6% per year and interest assumed in the cost of insurance is 4% per year. Cost of insurance is based on Makeham's mortality, H = 0.01+0.0001(1.05*). The account value at the beginning of the 7th year, before any premium is paid, is 1,500. Calculate, to the nearest integer, the account value at the end of the 7th year.arrow_forward
- If 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_forwardAn 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_forwardFinance Suppose that the spot price of copper is $3.25 per pound, the continuously compounded lease rate for copper is 4%, and the continuously compounded risk-free rate is 2%. Suppose that copper can be stored at zero cost. a)lf you short sell copper for one year, what is the total cash flow(including both the cost of returning the copper borrowed and any lease payment) to the copper lender at the end of the year? b)What is the 1-year forward price of copper? c)lf there are no arbitrage opportunities, what is the maximum possible 1-year forward price for copper? If the forward price were above this level, how could you take advantage of it?arrow_forward
- 6. 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_forwardThe 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_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
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage