Question

Find the present value of a deferred annuity of $500 a year for 6 years that is deferred 5 years if money is worth 6%

Please show work!

Answer 1

Assuming first payment made at the end of year 5.

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 at the end of Year4:

Particulars	Amount
Cash Flow	$               500.00
Int Rate	6.0000%
Periods	6

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 500 * [ 1 - [(1+0.06)^-6]] /0.06
= $ 500 * [ 1 - [(1.06)^-6]] /0.06
= $ 500 * [ 1 - [0.705]] /0.06
= $ 500 * [0.295]] /0.06
= $ 2458.66
Present Value Today:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$              2,458.66
Int Rate	6.0000%
Periods	6

Present Value = Future Value / ( 1 + r )^n
= $ 2458.66 / ( 1 + 0.06 ) ^ 6
= $ 2458.66 / ( 1.06 ) ^ 6
= $ 2458.66 / 1.4185
= $ 1733.26

Value of deferred annuity today is $ 1733.26