The inflation rate is a constant 3% a year, and the real interest rate is a constant 1% a year. How much must you have in your retirement account today if you want to make a withdrawal
Of $50,000 a year, quoted in today's dollars, each year after retirement for 25 years. Assume your
First withdrawal will be at the end of this year, and round your answer to the nearest thousand
Dollars.
A)$5,150,000
B)$780,000
C)$1,290,000
D)$1,105,000

Question

Quizplus · Accepted Answer

To find the present value of the withdrawals, we use the formula for the present value of an annuity. Given the inflation rate is 3% and the real interest rate is 1%, the nominal interest rate can be found using the Fisher equation: (1 + nominal rate) = (1 + real rate) * (1 + inflation rate), which gives a nominal rate of approximately 4%. Using the present value of an annuity formula: PV = PMT * [(1 - (1 + r)^-n) / r], where PMT = $50,000, r = 0.04 (4%), and n = 25 years, we calculate the present value. Plugging in the values, we get a present value close to $1,105,000 when rounded to the nearest thousand, which matches option D.

The Inflation Rate Is a Constant 3% a Year, and the Real