Topic 2 FINC 2011 Tutorial Solutions

Topic 2 FINC 2011 Tutorial Solutions - FINC 2011 Corporate...

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Tutorial Questions and Solutions Topic 2 – Review of Financial Mathematics PQ 7 What is the present value of a cash flow of $10,000 to be received in five years given   an interest rate of 6% p.a. over five years (a) compounded annually, (b) compounded  monthly, and (c) continuously compounded? A N S W E R (a) ( 29 58 . 472 , 7 $ 06 . 1 10000 1 5 = = + = n r FV PV For part (b) we have to divide the nominal annual interest rate by m , number of compounding periods in a year, to find the interest rate per compounding period ( r ), and we have to multiply the number of years by m to find the total number of periods. (b) ( 29 72 . 413 , 7 $ 005 . 1 10000 1 60 = = + = n r FV PV The present value is smaller with monthly compounding. This is because the initial amount would grow more quickly over the period of an investment because interest on interest is calculated and paid more frequently. To find the present value using continuous compounding, we use Equation 2.6. (c) ( 29 ( 29 18 . 408 , 7 $ 10000 5 06 . 0 = = = = e e FV PV PVe FV rt rt Clearly compounding occurs even more frequently under continuous compounding, and therefore the present value is even smaller than it was with monthly compounding. PQ 12 An investor is earning $15,000 this year but expects to be earning $60,000 next year.  What is the maximum amount that the investor can consume today if the interest rate  is 10%?   If the investor decides to consume zero this year, how much could she  consume next year? A N S W E R
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Topic 2 FINC 2011 Tutorial Solutions - FINC 2011 Corporate...

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