You are setting up a continuous annuity trust fund. Money is continuously transferred from your checking account to the trust fund at $1000.00 annually. The account earnes 8% interest compounded continually. Given A(0)=0 solve the differential equation for the amount, A, as a function of t
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You are setting up a continuous annuity trust fund. Money is continuously transferred from your checking account to the trust fund at $1000.00 annually. The account earnes 8% interest compounded continually. Given A(0)=0 solve the differential equation for the amount, A, as a function of t
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- An equation of the form y=7000 (1.09)* provides an example of interest compounded annually. This means that the full 9% of interest is added to the account at the end of one year. This doesn't sound very fair to someone that invests their money for 11 months-they get no interest at all. This became a competitive disadvantage for financial institutions, and some began to divide the annual interest into periodic shares, so that (for example) you could get 1/12th of that 9% each month. When this happens, we say that interest is compounded monthly. Interest can also be compounded weekly (52 times per year), quarterly (4 times per year), daily (365 times per year), or really any other period you could think of. If interest is compounded monthly, what growth factor would be needed to provide 1/12th of 9% interest each month? (Think about the difference between interest rate and growth factor.) The growth factor would be X SFind an expression for the present value of an annuity on which payments are 1 at the end of each 4-month period for 12 years assuming a rate of interest per 3-month period.For a simple interest loan with interest rater (expressed as a decimal), the amount A due at the end of t years on a principal P borrowed is P = A(1 + rt). (A) True B False
- What is the compound amount factor (CAF) if I is the interest rate per year, m is a number of periods per years, n is the number of periods and the interest rate is paid more than once in a year? a) | 1+ i b) | 1+. n c) | 1+ n d) | 1+Suppose that $500 is invested at the end of every year for 5 years. The polynomial function that models the value of the investment is P(x) = 500x5 + 500x4 + 500x³ + 500x² + 500x, where x represents the effective interest rate plus 100%. One year after the last payment, the investment is worth $3200. Find the effective interest rate one year after the last payment, to the nearest tenth. (Note: You will need to subtract 1 from the value of x to find the effective interest rate.)To make CDs look more attractive as an investment than they really are, some banks advertise that their rates are higher than their competitors' rates; however, the fine print says that the rate is based on simple interest. If you were to deposit $16,000 at 10.00% per year simple interest in a CD, what compound interest rate would yield the same amount of money in 3 years? (Round the final answer to three decimal places.) The compound interest rate that would yield the same amount of money in 3 years is % per year.
- In 1915, Albert Epstein allegedly borrowed $7,000 from a large New York bank on the condition that he would repay 7% of the loan every three months, until a total of 50 payments had been made. At the time of the 50th payment, the $7,000 loan would be completely repaid. Albert computed his annual interest rate to be [0.07($7,000) × 4]/$7,000 = 0.28 (28%). Solve, (a) What true effective annual interest rate did Albert pay? (b) What, if anything, was wrong with his calculation?Consider the following two cash flow series of payments: Series A is a geometric series increasing at a rate of 6.5% per year. The initial cash payment at the end of year 1 is $1,000. The payments occur annually for 5 years. Series B is a uniform series with payments of value X occurring annually at the end of years 1 through 5. You must make the payments in either Series A or Series B. Determine the value of X for which these two series are equivalent if your TVOM is i = 8.5 %. If your TVOM is 8%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice. PW, Series A: PW, Series B: If your TVOM is 5%, would you be indifferent between these two series of payments? Enter the PW for each series to support this choice. PW, Series A: PW, Series B: Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely.…A geometric gradient that increases at f= 8% per year for 12 years is shown in the accompanying diagram. The annual interest rate is 12%. What is the present equivalent value of this gradient?
- Suppose a relative has promised to give you $1,000 as a wedding gift the day you get engaged. Assuming a constant interest rate of 5%, consider the present and future values of this gift, depending on when you become engaged. Complete the first row of the following table by determining the value of the gift in one and two years with interest if you become engaged today and save the money. Date Received Present Value Value in One Year Value in Two Years (Dollars) (Dollars) (Dollars) Today 1,000.00 In 1 year 1,000.00 In 2 years 1,000.00 Now complete the first column of the previous table by computing the present value of the gift if you get engaged in one year or two years. The present value of the gift is if you get engaged in two years than it is if you get engaged in one year.2) An account earns (12) 2% for the first two years, (12) 3% for the net two years, and ;(12) = 6% for the last year. Find the accumulated value of a five year annuity that pays $200 at the end of each month.← Use graphical approximation techniques to answer the question. When would an ordinary annuity consisting of quarterly payments of $430.20 at 8% compounded quarterly be worth more than a principal of $4600 invested at 5% simple interest? The annuity would be worth more than the principal in approximately (Round to one decimal place as needed.) years.
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