Today, you retire with $1,200,000 and you want to ensure that you can withdraw $1500 per...

Today, you retire with $1,200,000 and you want to ensure that you can withdraw $1500 per week (52 weeks per year) and plan to earn a 4% rate of return. How many weeks will your original $1,200,000 last?

Expert Solution

Amount Available = $1,200,000

P = Weekly withdrawl = $1,500

r = weekly interest rate = 4%/52 = 0.076923%

n = number of weeks

Number of weeks can be calculated using the below formula

PV = P * [1 - (1+r)^-n] / r

$1,200,000 = $1,500 * [1 - (1+0.076923%)^-n] / 0.076923%

$923.076923077 = $1,500 * [1 - (1.00076923)^-n]

1 - (1.00076923)^-n = 0.61538461538

(1.00076923)^-n = 0.38461538462

(1.00076923)^n = 2.60

n = log (2.60) / log(1.00076923)

n = 1242.64381867 weeks

Therefore, original amount will last for 1,243 weekd

jeff jeffy answered 2 years ago

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