Question

Please make sure to complete all parts of the question and to show all work used to compute the answer so I can see how the answer was found.

A five-year annuity of 10 $5,230 semiannual payments will begin nine years from now, with the first payment coming nine and a half years from now. If the discount rate is 10 percent compounded monthly, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?

Answer 1

Discount rate per annum is 10% per annum compounded monthly hence effective semi-annual rate shall be:

.= (1+.1/12)^{^6}-1

=1.0510533133-1

=.0510533133 or 5.11% approx

And Effective annual rate shall be=(1+.1/12)^{^12}-1

=.104713 or 10.4713%

Computation of value of annuity at the end of 9th year = Annuity(i.e. semiannual payments) * PV factor of [email protected]% per semiannual for 10 periods

=5230*7.682389

=40178.89

Years left at the end of 5th year shall be 4years(i.e.9-5).

Computation of value of annuity at the end of 5th year = Value of annuity at 9th year end*PV factor of $1 @ 10.4113% receivable in 4 years

=40178.89 * [1/(1+.104713)^4]

=40178.89*.671432

=26977.3952

Years left at the end of 5th year shall be 6years(i.e.9-3).

Computation of value of annuity at the end of 3rd year = Value of annuity at 9th year end*PV factor of $1 @ 10.4113% receivable in 6 years

=40178.89 * [1/(1+.104713)^{^6}]

=40178.89*.550178

=22105.544

Computation of value of annuity now(i.e. at period 0)=Value of annuity at 9th year end*PV factor of $1 @ 10.4113% receivable in 9 years

= 40178.89*.408089

=16396.565

Hence current value of annuity is $16396.565

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