Question

A 15-year annuity of thirty $8,000 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now. a. If the discount rate is 12 percent compounded monthly, what is the value of this annuity 8 years from now? b. What is the current value of the annuity?

Answer 1

Annuity begins 11 years from now, so first we will find value of annuity at the end of 11th year.

Discounting rate = 12% p.a. compounded monthly

Therefore Semi-annual discounting rate (I)= (1+12%/12)6 - 1 = 6.152% per semi-annum

Semi-annul annuity payment (PMT) = $8000

No of semi-annual annuities (N) = 30

Therefore Present Value of annuity that is value of annuities at the end of 11th year (PV) = ?

Using financial calculator or PV function in excel,

Therefore, value of annuities at the end of 11th year (PV) = $108,350.40

Value of annuity at the end of 8th year = value at the end of 11th year / (1+i)n

Therefore value of annuity at the end of 8th year = 108,350.40 / (1+6.152%)6

{n is 6 since discount rate is semi-annual so for 3 years from year 8 to 11, there are 6 semi-annums}

Therefore value of annuity at the end of 8th year = $75,728.80

Current Value of annuity = value at the end of 11th year / (1+i)n

Therefore Current value of annuity = 108,350.40 / (1+6.152%)22

{n is 22 since discount rate is semi-annual so for 11 years from year 0 to 11, there are 22 semi-annums}

Therefore Current value of annuity = $29,134.61

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