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- 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.)4. If 10,000php is invested in account paying 6% compounded quarterly; A. How much will be in the account at the end of 5years? b. How much interest will it earn? C. Compare the interest it will earn if it is paid at simple interest rate.How much compound interest is earned on a 6.5-year investment that has a rate of return of 6%compounded quarterly and repays a total compound amount (future value) of$9,600?
- 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 of $15,785 is accumulated at 6.5% compounded quarterly for 5 years. At that time the interest rate is changed to 4.3% compounded monthly. How much is the investment worth after 10 years? Answer to the nearest cent.For a sum of 1,050 to triple itself in 8 years and 6 months, what must be the rate of interest compounded semi-annually? (Finding the rate by linear interpolation)
- For a sum of money invested at 11.5% compounded for 5 years state the following values. i) The number of compounding periods is =? ii) The periodic rate of interest is = %? iii) The compounding factor is (1+?)? iv) The numerical value of the compounding factor is =?Using an effective rate of interest of 8% per annum, calculate the CONVEXITY of the following series of payments: £300 payable after 4 years, £200 payable after 12 years, and £250 payable after 17 years.Suppose that $1,000 is invested for 4 years at an interest rate of 12%, compounded quarterly. How much will be in the account at the end of 4 years?
- Assume that time is measured in years. Calculate the total present value at time 0 of a payment of £257 paid at time 4 and a payment of £67 paid at time 12, using an interest rate of 5% per annum effective.1. What interest comp. monthly is equivalent to an interest rate of 14.5% comp. quarterly? 2. A sum of $145,000 is invested now and left for 8 years, at which time the principal is withdrawn. The interest that has accrued is left for another 8 years. If the interest rate is 5%, what will be the withdrawal amount at the end of the 16th year? 3. How long will it take for an investment to increase by 145% its amount if money is worth 14% comp. semi-annually? 4. A man makes a payment of $1450 at the beginning of every month on a bank that offers 6% interest. How much did the man borrow if the payment would last for 10 years? 5. A young woman made a loan from a certain bank and started paying $1450 quarterly after 2 years from the loan date. If payment is to be made for 5 years and interest is 10%, how much was loaned by the woman?The interest on a particular savings account is compounded continuously. The account initially had $2,200 deposited in it. The worth of the account after t-years can be calculated using the formula: A(t)=2200e0$1 (a) By what percent will the worth of the account increase per year? Round to the nearest hundredth of a percent. (b) To the nearest tenth of a year, how long will it take for the worth of the account to triple? (c) If another investment began with a principal of $2,500 and earned simplest interest of 3.8% applied once per year, which investment would be worth more after 10 years? Justify
