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?
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- A certain some of money P draws interest compounded continuously. If a certain time there are Po dollars in the account, determine the time when the financial attains the value of 2Po dollars if the annual interest rate at 2%You have been depositing money into an account yearly based on the following investment amounts, rates and times. What is the value of that Investment account at the end of that period?*Using Matlab* 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)^(nt) 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?
- 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?All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 8%, or 16%. Identify the interest rate that corresponds with each line. VALUE (Dollars) Line A: 01 2 3 4 5 Line B: 6 B Line C: C 7 8 9 10 TIME (Years) Investments and loans base their interest calculations on one of two possible methods: the interest and the interest methods. Both methods apply three variables-the amount of principal, the interest rate, and the investment or deposit period to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.For the following exercise, use the compound interest formula, A(t) = P 1 + r n nt , where money is measured in dollars.After a certain number of years, the value of an investment account is represented by the expression 10,950 1 + 0.03 2 24 . How many years had the account been accumulating interest? yr
- When $8,600 is invested in a savings account paying simple interest for the year, the interest, i in dollars, can obtained from the equation i=8,600r, where r is the rate of interest in decimal form. Graph i=8,600r, for r up to including a rate of 16%. If the rate is 7%, how much interest is earned? OA. $6,020 OB. $602 O C. $586 OD. $622 ITo calculate how many years (n) an investment (P) must be kept in an account that earns interest at i%, in order to triple in amount, which of the following expressions should be used? (a) n = -P + F(P/F, i%, n) (b) n = [log (F/P)]/[log (1+ i%)] (c) n = [ In(– P +F)]/[In i%] (d) n = -F(1 + i%)PSavings institutions often state a nominal rate, which can be thought of as a simple annual interest rate, and the effective interest rate, which is the actual interest rate earned due to compounding. Given the nominal rate, it is easy to calculate the effective interest rate as follows. Assume that $1 is invested in an account paying an interest rate of 6% compounded monthly. Using the compound interest formula A =P 1+ m with P = 1, r =0.06, m 12, and n 12 0.06 = 12, A =1 + 12 1.0617. So the effective interest rate is 1.0617 - 1 = 0.0617, or 6.17%. Find the effective interest rate for the investments with a nominal yield of 10%, compounded quarterly. The effective annual yield is %. (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer. Check Answer All parts showing Clear All javascript:doExercise(12); avascript:doExercise(14); Type here to search
- 3. Future value The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value. The process for converting present values into future values is called four time-value-of-money variables. Which of the following is not one of these variables? O The present value (PV) of the amount invested O The duration of the investment (N) O The interest rate (I) that could be earned by invested funds O The inflation rate indicating the change in average prices This process requires knowledge of the values of three ofSuppose that P dollars in principal is invested in an account earning 2.1% interest compounded continuously. At the end of 2 yr, the amount in the account has earmed $193.03 in interest. a. Find the original principal. Round to the nearest dollar. (Hint: Use the model A = Pe" and substitute P + 193.03 for A.) b. Using the original principal from part (a) and the model A = Pe", determine the time required for the investment to reach $6000. Round to the nearest tenth of a year.Savings institutions often state a nominal rate, which can be thought of as a simple annual interest rate, and the effective interest rate, which is the actual interest rate earned due to compounding. Given the nominal rate, it is easy to calculate the effective interest rate as follows. Assume that $1 is invested in an account paying an interest rate of 6% compounded monthly. Using the compound interest formula A = P 1+ with P 0.06) 12 = 1, r = 0.06, m = 12, and n = 12, A = |1+ rate is 1.0617 -1= 0.0617, or 6.17%. Find the effective interest rate for the investments with a nominal yield of 10%, compounded quarterly. s 1.0617. So the effective interest 12 The effective annual yield is%. (Round to two decimal places as needed.)