You are offered an annuity that will pay you $10,000 at the end of each year for 20 years, with the first payment being in 10 years from today.

You are offered an annuity that will pay you $10,000 at the end of each year for 20 years, with the first payment being in 10 years from today. If the interest rate is 12% annually, what is the annuity worth to you today?

Expert Solution

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

PV of Annuity after 9 Years:

Particulars	Amount
Cash Flow	$ 10,000.00
Int Rate	12.0000%
Periods	20

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 10000 * [ 1 - [(1+0.12)^-20]] /0.12
= $ 10000 * [ 1 - [(1.12)^-20]] /0.12
= $ 10000 * [ 1 - [0.1037]] /0.12
= $ 10000 * [0.8963]] /0.12
= $ 74694.44
PV Today:

Particulars	Amount
Future Value	$ 74,694.44
Int Rate	12.0000%
Periods	9

Present Value = Future Value / ( 1 + r )^n
= $ 74694.44 / ( 1 + 0.12 ) ^ 9
= $ 74694.44 / ( 1.12 ) ^ 9
= $ 74694.44 / 2.7731
= $ 26935.56

Present Value of Annuity Today is $ 26935.56

jeff jeffy answered 1 year ago

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