Question

PLEASE SOLVE THIS QUESTION IN DETAILS AND WITHOUT USING FINANCIAL CALCULATOR, AGAIN DO NOT USE FINANCIAL CALCULATOR:

Today, you are retiring. You have a total of $411,016 in your retirement savings and have the funds invested such that you expect to earn an average of 7.10 percent, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money?

Answer 1

PV of Retirement fund = 411016
Rate per month =7.10/12%
Amount to withdraw at beginning of every month = 2500

PV using annuity due formula = (1+r)*PMT*(1-(1+r)^-n)/r
411016 =(1+7.10%/12) *2500*(1-(1+7.10%/12)^-n)/7.10%
411016*7.10%/(12*2500)/(1+7%/12) = (1-1.005917^-n)
0.9727/(1+7%/12) = 1-1.005917^-n
1.005917^-n = 1-0.967096
1.005917^-n =0.032904
Applying log on both sides
n =- log(0.032904)/log(1.005917) = 578.33688

Number of Years =578.33688/12 =48.19 years