Question

You plan to retire at age 65. You want to withdraw $100,000 from your savings account every year starting on your 65 th birthday. You expect to make your final withdrawal on your

84^th birthday. How much must you have accumulated by your 65 th birthday in order to support your desired withdrawals if you earn 3% on your savings?

$1,090,095.56

B.

$1,587,747.49

C.

$1,532,379.91

D.

$1,432,379.91

E.

$1,475,351.31

What is the present value of a $50 perpetuity if interest rates are 7%?

$3.50

B.

$18.12

C.

$714.29

D.

$1.21

E.

$593.23

Answer 1

Solution to the QUESTION-1

The Present Value of an Ordinary annuity

Annual Payment (P) = $100,000

Annual interest rate (r) = 3.00% per year

Number of years (n) = 19 Years [84 Years – 65 Years]

Therefore, the Present Value of an Ordinary annuity = P x [{1 - (1 / (1 + r) n} / r]

= $100,000 x [{1 - (1 / (1 + 0.03)19} / 0.03]

= $100,000 x [{1 - (1 / 1.753506053)} / 0.03]

= $100,000 x [(1 - 0.570286027) / 0.03]

= $100,000 x [0.429713973 / 0.03]

= $100,000 x 14.32379911

= $1,432,379.91

Solution to the QUESTION-2

The Present Value of the Perpetuity = Annual payment / Discount rate

= $50.00 / 0.07

= $714.29