Question

A 10-year annuity of 20 $8,900 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now. If the discount rate is 8 percent compounded semiannually, what is the value of this annuity ten years and eight years from now? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) What is the value of the annuity today?

Answer 1

The question is based on the time value of money.

Step-1:Calculation of Value of annuity 11 years from now

Present value of annuity 11 years from now

=

Annuity x Present Value of annuity of 1

=

$             8,900

x

13.59033

=

$ 1,20,953.90

Working:

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.04)^-20)/0.04

i

8%/2

=

0.04

=

13.59033

n

10*2

=

20

Step-2:Calculation of Value of annuity 10 years from now

Present Value

=

Above Value x Discount factor

=

$ 1,20,953.90

x (1.04^-2)

=

$ 1,11,828.68

Step-3:Calculation of value of annuity 8 years from now

Present Value

=

Above Value x Discount factor

=

$ 1,11,828.68

x (1.04^-4)

=

$     95,591.63

Step-4:Calculation of Value of annuity today

Value of annuity today

=

Above Value x Discount factor

=

$     95,591.63

x (1.04^-16)

=

$     51,037.15

Thus

Present Value of annuity

Value of annuity ten years from now

$ 1,11,828.68

Value of annuity eight years from now

$     95,591.63

Value of annuity today

$     51,037.15