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**Unformatted text preview: **6-20NOMINAL COMPOUNDINGa.It is now January 1, 2003. You plan to make 5 deposits of $100 each, one every 6 months, with the first payment being made today. IF THE BANK PAYS A NOMINAL INTEREST RATE OF 12 PERCENT, BUT USES SEMIANNUAL COMPOUNDING, HOW MUCH WILL BE IN YOUR ACCOUNT AFTER 10 YEARS?b.Ten years from today you must make a payment of $1,432.02. To prepare for this payment, you will make 5 equal deposits, beginning today and for the next 4 quarters, in a bank that pays a nominal interest rate of 12 percent, quarterly compounding. HOW LARGE MUST EACH OF THE 5 PAYMENTS BE?(a.)Begin with a time line:0 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 6-mos.0 6% 1 2 3 4 5 8 9 10 Years. . .100 100 100 100 100 FVASince the first payment is made today, we have a 5-period annuity due. The applicable interest rate is 12%/2 = 6%. First, we find the FVA of the annuity due in period 5 by entering the following data in the financial calculator:N=5I=12/2=6PV=andPMT=-100Setting the calculator on BEG, we find FVA (Annuity due) = $597.53. Now, we must compound out for 15 semiannual periods at 6 percent.$597.53 20 - 5 = 15 periods @ 6% $1,432.02.(b.)0 3% 1234540 quarters. . .PMTPMTPMT PMTPMTFV = 1,432.02The time line depicting the problem is shown above. Because the payments only occur for 5 periods throughout the 40 quarters, this...

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