Question

A 7-year annuity of fourteen $9,000 semiannual payments will begin 13 years from now, with the first payment coming 13.5 years from now.

   

a.	If the discount rate is 12 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	If the discount rate is 12 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	If the discount rate is 12 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

    

Answer 1

Semiannual annuity of $9,000 for 7 years starting from 13.5 years from now.

Discount rate used = 12%

PV of the annuity payments on year 13 = PV of Cash Flow at Year 13.5 + PV of Cash Flow at Year 14 + PV of Cash Flow at Year 14.5 + ... + PV of Cash Flow at Year 20

= 9000/(1 + (0.12/12))^(0.5*12) + 9000/(1 + (0.12/12))^(1*12) + 9000/(1 + (0.12/12))^(1.5*12) + ... + 9000/(1 + (0.12/12))^(7*12)

= $82,873.0213

(a)

Now Consider this PV at year 13 as any other cash for example where there is a single cash flow at year 13 with discount rate of 12% monthly compounded.

Therefore PV at Year 3 = Cash Flow/(1 + (Discount rate/Period of Compounding))^(Years in Discounting*Period of Compounding)

{Now the Years in Discounting is the number of years to discount}

= $82,873.0213/(1 + (0.12/12))^(8*12)

= $31,833.15

(b)

Therefore PV at Year 3 = Cash Flow/(1 + (Discount rate/Period of Compounding))^(Years in Discounting*Period of Compounding)

{Now the Years in Discounting is the number of years to discount}

= $82,873.0213/(1 + (0.12/12))^(10*12)

= $25,110.09

(c)

Therefore PV at Year 3 = Cash Flow/(1 + (Discount rate/Period of Compounding))^(Years in Discounting*Period of Compounding)

{Now the Years in Discounting is the number of years to discount}

= $82,873.0213/(1 + (0.12/12))^(13*12)

= $17,550.07