Question

Show work how to solve to get the answer.

1. I plan to retire in 25 years, and after I retire, I want to be able withdraw $6000 per month for 35 years. My account earns a nominal rate of 6 percent, compounded monthly. How much do I need in my account when I retire? $1, 052,281.36

2.  I plan to retire in 25 years, and when I retire, I want to be able withdraw $6000 per month for 35 years. My account earns a nominal rate of 6 percent, compounded monthly. How much must I save each month to meet my retirement objective?$1518.46

3.  I plan to retire in 25 years, and when I retire, I want to be able withdraw $6000 per month for 35 years. My account earns a nominal rate of 6 percent, compounded monthly. How much must have I save each month to meet my retirement objective if I make my payments into my retirement account at the beginning of the month, rather than at the end? $1510.91

Answer 1

1. Number of Periods = 35*12 = 420
Rate per month = 6000
Rate per month = 6%/12 = 0.5%
PV using annuity formula = PMT*(1-(1+r)^-n)/r = 6000*(1-(1+0.5%)^-420)/0.5% = 1,052,281.36

2. Value at retirement = 1,052,281.36
Rate per month = 6%/12 = 0.5%
Number of Periods = 12*25 = 300
Savings per month (PMT) using annuity of FV= 1,052,281.36/((1+0.5%)³⁰⁰-1)/0.5% = 1518.46

3. If payment is paid per month at the beginning using annuity due of FV =(1+.5%)*1,052,281.36/((1+0.5%)³⁰⁰-1)/0.5% = 1510.90

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well