Question

(Present value value of an annunity) What is the presnt value of the following annuities ?

a. $2,400 a year for 8 years discounted back to the presnet at 9 percent.

b. $90 a year for 5 years discounted back to the present at 8 percent.

c. 270$ a year for 12 years discounted back to the present at 12 percent.

d. 450$ a year for 6 years discounted back to the present at 5 percent

A.) What is the present value at $2,400 a year for 8 years discounted back to the present a 9 percent? $() round to nearest cent

B.)What is the present value at $90 a year for 5 years discounted back to the present at 8 perecent ? $() round to nearest cent

C.) What is the present value at $270 a year for 12 years discounted back to the present at 12 percent? () round to nearest cent

D.)What is presnt value at $450 a year for 6 years discounted back to the present at 5 perecent ? () round to nearest cent

Answer 1

a.

Present Value of annuity

$ 13,283.57

Working:

1)

Present value of annuity of 1

=

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

where,

=

(1-(1+0.09)^-8)/0.09

i

9%

=

5.53481911

n

8

2)

Present Value of annuity

=

Annual cash flow x Present Value of annuity of 1

=

$         2,400

x

5.534819

=

$ 13,283.57

b.

Present Value of annuity

$       359.34

Working:

1)

Present value of annuity of 1

=

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

where,

=

(1-(1+0.08)^-5)/0.08

i

8%

=

3.99271

n

5

2)

Present Value of annuity

=

Annual cash flow x Present Value of annuity of 1

=

$               90

x

3.99271

=

$       359.34

c.

Present Value of annuity

$   1,672.48

Working:

1)

Present value of annuity of 1

=

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

where,

=

(1-(1+0.12)^-12)/0.12

i

12%

=

6.19437

n

12

2)

Present Value of annuity

=

Annual cash flow x Present Value of annuity of 1

=

$             270

x

6.19437

=

$   1,672.48

d.

Present Value of annuity

$   2,284.06

Working:

1)

Present value of annuity of 1

=

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

where,

=

(1-(1+0.05)^-6)/0.05

i

5%

=

5.07569

n

6

2)

Present Value of annuity

=

Annual cash flow x Present Value of annuity of 1

=

$             450

x

5.07569

=

$   2,284.06