Use the RSTUV method to obtain the solution. If P dollars are invested at r percent compounded annually, then at the end of 2 years, the amount will have grown to A = P(1 + r)2. At what rate of interest will $1000 grow to $1123.60 in 2 years? %
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- (1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually? (2) What is the PV of the same stream? (3) Is the stream an annuity? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when INOM = EFF% = IPER.) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM/2 = 10%/2 = 5%?When an initial amount of P dollars is invested at r% annual interest compounded n times per year, the value of the account (4) after years is given by the equation nt A=P(1 + =)** n Write an equation that represents the value in an account that starts out with an initial investment of $5000 and pays 10% interest compound monthly. Then use that equation to fill the table and use the table to graph the equation. Years (1) Value (4) 0 5 10 15 20 oo → KISuppose $100 is invested at the end of each year for the next 5 years into an account paying an interest rate r% p.a. How much can be drawn at the end of the 5 years?Approach(i) The first $100 is contributed in one year’s time and has to wait 4 years to “mature”. Write an equation describing this.(ii) The second $100 is contributed in two year’s time and has to wait 3 years to “mature”. Write an equation describing this.
- Suppose $100 is invested at the end of each year for the next 5 years into an account paying an interest rate r% p.a. How much can be drawn at the end of the 5 years? Approach (i) The first $100 is contributed in one year's time and has to wait 4 years to "mature". Write an equation describing this. (ii) The second $100 is contributed in two year's time and has to wait 3 years to "mature". Write an equation describing this. (iii) The third $100 is contributed in three year's time and has to wait 2 years to "mature". Write an equation describing this. (iv) Continue with this logic and sum all the matured values expressed1. (See image), which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t), in years is given by the function. Thus if you invested $100 now at the annual rate of 5 1/2% for 6 years and 3 months you would get back (at the end of the time), F = $100e^(0.055)^(6.25) = $100e^(0.3438) = $100(1.4102) = $141.02. Suppose you put $2000 in a savings account when your son was born for 18 years and 6 months to help pay for his college education. If you can earn 3% annually on it, what should you have in his education savings account in 18 years and 6 months?set up an equation and solve each problem. Suppose that $500 is invested at a certain rate of interest compounded annually for 2 years. If the accumulated value at the end of 2 years is $594.05, find the rate of interest.
- Use the model A-Pe' or 4-P(1+)".- for years. where is the future value of P dollars invested at interest rater compounded continuously or x times per year If $8000 is put aside in a money market account with interest compounded monthly at 2.5%, find the time required for the account to earn $2000. Round to the nearest month. It will take approximately 6 years and 8 months for the account to earn $2000.Find the present value PV of the annuity account necessary to fund the withdrawal given. HINT [See Quick Example 3.] (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $2,800 per quarter for 10 years, if the account earns 6% per year PV = $ Need Help? Read ItApproximately, what is the value of (P) if F=9540, n=2 years, and i= 2.5% per year?
- b1. F = Pert , which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t), in years is given by the function. Thus if you invested $100 at the annual rate of 5 1/2% for 6 years and 3 months you would get back (at the end of the time), F = $100e(0.055)(6.25) = $100e(0.3438) = $100(1.4102) = $141.02. If you invest $15000 today, what amount does the formula say you will get back if you leave it for 5 years and 3 months in a savings account paying 4 1/2% annually?Use the formula A = Pert to find the future value after 20 years of a $7,000 account that earns 8% interest compounded continuously, then compare that to the future value of the same account if interest is compounded annually. Round to the nearest cent. The future value of the account with interest compounded continuously is The future value of the account with interest compounded annually is The account earns $____ (what dollar amount) [more/less] when interest is compounded continuously %241. This problem relates to Future Value, and Future income streams. Assume continuous compounding of interest. (a) Find the present value of a single future payment of FV = $50,000 to be made 20 years from now, assuming an interest rate of 5 percent. (b) Suppose you want a future income stream (annual payments) of FV (t) = 500t for 20 years. Find the present value of this income stream, assuming an interest rate of 5 percent.
