1.6 Today you have P to invest in a security that pays an interest rate of r per year and compounds in k periods. Find the formula to determine how long it will take this investment to grow to xp? Does the length of time depend on the initial amount P? • How long will it take to double the investment of $1000 where r is 6% with daily compounding? How long will it using the simple interest rate when r is 6% ?

1.6 Today you have P to invest in a security that pays an interest rate of r per year and compounds in k periods. Find the formula to determine how long it will take this investment to grow to xp? Does the length of time depend on the initial amount P? • How long will it take to double the investment of $1000 where r is 6% with daily compounding? How long will it using the simple interest rate when r is 6% ?

Financial Management: Theory & Practice

16th Edition

ISBN:9781337909730

Author:Brigham

Publisher:Brigham

Chapter4: Time Value Of Money

Section: Chapter Questions

Problem 12MC: (1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest...

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Define the stated (quoted) or nominal rate INOM as well as the periodic rate IPER. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why? What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?
(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%?
a) At what annual interest rate would the following have to be invested? i) $500 to grow to $1,948.00 in 12 years ii) $300 to grow to $422.10 in 7 years iii) $50 to grow to $280.20 in 20 years iv) $200 to grow to $497.60 in 5 years b) You are considering invest ing in a security that will pay you $1,000 in 30 years. i) If the appropriate discount rate is 10 percent, what is the present value of this investment? ii) Assume these securities sell for $365, in return for which you receive $1,000 in 30 years. What is the rate of return investors earn on this security if they buy it for $365? USE EXCEL TO WORK THIS OUT AND SHOW THE FORMULA!
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a ) How much money has to be invested today in a security that promises to pay 20000 Omani Riyals at the end of 6 years ? Assume that you can eam 10 % interest compounded per am b ) Suppose interest rate increase to 20 % mswer the question again and compare answers
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You investe an amount of P50,000 with a promised interest of 9% compounded quarterly. How many years will it take for the money to become twice the original amount? What is the effective interest rate? Taking into consideration the inflation rate which is 6%, what is the actual purchasing power of your investment by the time you choose to withdraw it?
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