Question

A 20-year annuity of forty $6,000 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. Required : (a) If the discount rate is 13 percent compounded monthly, what is the value of this annuity 5 years from now? (Click to select) (b) What is the current value of the annuity? (Click to select)

Answer 1

Effective Rate for 6 months:

Particulars	Amount
Ret period	1.0833%
No. of periods	6.0000

Effective Rate for 6 months = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.010833 ) ^ 6 ] - 1
= [ ( 1.010833 ) ^ 6 ] - 1
= [ 1.0668 ] - 1
= 0.0668
I.e Effective rate for 6 months is 6.68 %

PV of annuity after 9Years:

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 = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 6000 * [ 1 - [(1+0.0668)^-40]] /0.0668
= $ 6000 * [ 1 - [(1.0668)^-40]] /0.0668
= $ 6000 * [ 1 - [0.0753]] /0.0668
= $ 6000 * [0.9247]] /0.0668
= $ 83058.68

PV of annuity after 5 Years:

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	$            83,058.68
Int Rate	6.6800%
Periods	8

Present Value = Future Value / ( 1 + r )^n
= $ 83058.68 / ( 1 + 0.0668 ) ^ 8
= $ 83058.68 / ( 1.0668 ) ^ 8
= $ 83058.68 / 1.6775
= $ 49513.2

Present value after 5 Years is $ 49513.20

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	$            83,058.68
Int Rate	6.6800%
Periods	18

Present Value = Future Value / ( 1 + r )^n
= $ 83058.68 / ( 1 + 0.0668 ) ^ 18
= $ 83058.68 / ( 1.0668 ) ^ 18
= $ 83058.68 / 3.2025
= $ 25935.28