Question

1. Your father is about to retire, and he wants to buy an investment that will provide him with $100,000 of income per year for 20 years, beginning a year from today. In addition, on the 20th anniversary (when the last payment of $100,000 occurs), he wants to withdraw a lumpsum of $250,000 (in addition to the last receipt of$100,000). The going rate on such annuities is 4.0%. How much would it cost him to buy such an annuity today (in $’000s)? a. $1,124.0 b. $1,224.9 c. $1,340.4 d. $1,473.1 e. $1,626.2

Answer 1

d. $1,473.1

Cost of annuity is the present value of cash flows from annuity.

Step-1:Calculation of present value of per year cash flows over 20 years

Present Value

=

Yearly cash flows * Present value of annuity of 1

=

$    1,00,000.00

*

13.59032634

=

$ 13,59,032.63

Working:

Present value of annuity of 1

=

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

Where,

=

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

i

4%

=

13.59033

n

20

Step-2:Calculation of present value of other payment on 20th year

Present value

=

Cash flows at the end of year 20 * Present Value of 1 to be recived at the end of Year 20

=

$          2,50,000

*

0.456386946

=

$    1,14,096.74

Working:

Present Value of 1

=

(1+i)^-n

Where,

=

(1+0.04)^-20

i

4%

=

0.456386946

n

20

Step-3:Calculation of present value of all future Cash flows

Present Value of annual payment over 20 years

$ 13,59,032.63

Present value of single payment at the end of 20 Year

$    1,14,096.74

Present Value of all future cash flows

$ 14,73,129.37

Thus,

Cost of such annuity

=

$ 14,73,129.37

or

$          1,473.13

(in $'000)