pose Find the exponential function that describes the amount in the account after time t, in year: What is the balance after 1 year? 2 years? 5 years? 10 years? What is the doubling time?
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- Suppose that $18,982 is invested at an interest rate of 5.6% per year, compounded continuously a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time?4) A savings account balance is compounded continuously. If the interest rate is 3.1% per year and the current balance is $1077.00, in how many years will the balance reach $1486.73?The value of a bank account collecting interest which is continuously compounded is modeled by the equation: A = Pet where: A is the value of the account at time t P, or the principal, is the value of the initial investment t is time (measured in years) r is the interest rate (written as a decimal) 1. Suppose that $5000 is put into an account with an interest rate of 8% compounded continuously. a) How much will the account be worth after 3 years (exact value) ? b) How much will the account be worth after 3 years (rounded to the nearest cent) ? c) How many years will it take for the value of the account to double? In an exponential model for population growth, the size of a population at time t is rt described by the equation: N(t) = Net where: N is the initial population or the population at t=0 r is the percentage growth rate t = time and can be measured in different units depending on the problem. Note: You don't have to use e and r. It is often possible to find an equivalent form…
- Suppose that $1,000 is invested at 6% interest compounded continuously. Use the formula A = Pert. (a) How long (to the nearest day) before the value is $1,250? (answer should be in years, days) (b) How long (to the nearest day) before the money doubles? (answer should be in years, days)When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 3 years when $6000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (Round your answer to the nearest cent.) b) in how many years will the initial sum deposited have doubled?(round to the nearest year) c) use a calculator to compare the amount obtained in part (a) with the amount s=(1 + 1/4(0.0575))^3(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.)1.) What is the rate annually that will produce the same amount of interest per year is called? 2.) Its the total amount to be paid or received after a given period of time? 3.) What do you call the number of conversion that take place in a year 4.) What do you call the time interval between succeeding interest calculations?
- An investment is represented by the equation A(t)=10,250(1+ 0.04/12)120 How many years has the account been accumulating interest?Example 1. Compound interest When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is, dx/dt = rx. (a) If $2000 is invested at 8%, compounded continuously, find an equation for the future value of the investment as a function of time t, in years. (b) How long will it take for the investment to double? (c) What will be the future value of this investment after 35 years?The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
- An investment becomes P 4,500,000 four years from now and becomes P 5,250,000 thirteen years from now. a. Assuming rate of compounded interest remains constant through time, what was the investment's value on the present time? b. What rate of interest compounded quarterly is equivalent to the interest rate of the given investment? c. What rate of interest compounded monthly is equivalent to the interest rate of the given investment?The Future value of a Present amount of money (compounded annually) after 1 year can be determined by: multiplying the Present amount by (1+interest rate) dividing the Present amount by (1+interest rate) adding the interest rate to the Present amount subtracting the interest rate from the Present amount(a) Find the present and future value of an income stream of $6000 per year for a period of 10 years if the interest rate, compounded continuously, is 2%. Round your answers to two decimal places. Present value = $ Future value $ (b) How much of the future value is from the income stream? How much is from interest? Round your answers to two decimal places. The amount from the income stream is $ The amount from the interest is $