15 year annuity of 30 semiannual payments

QUESTION

A 15-year annuity of 30 semiannual payments of $11,000 each will begin 9 years from now, with the first payment coming 9.5 years from now. If the discount rate is 7 percent compounded monthly, what is the value of this annuity 6 years from now? What is the current value of the annuity?
Semi annual rate =0.11/2=0.055
PVa= C (1-[1/(1 R)]^t/r)
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= 9000 (1-[1/(1 1.055)]^10/0.055)= 67 838.63
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This is the present value one period before the first payment. The first payment occurs nine nad one half years from now. So this is the vakue of the annuity nine years from now. Since the interest rate is semi annula , we must also be careful to use the number odf semiannual periods . the value of the annuity five years from now is
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PV= FV /(1

t
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PV=67 838 /(1 0.055)^8=44,203.58
And the value of annuity three years from now is PV= FV /(1 r)^t
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=67838 /(1 0.055)^12=35,681.87
And the value of annuity today is PV= FV /(1 r)^t
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=67838 /(1 0.055)^18=25878.13
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ANSWER:

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