Question

You plan on starting a retirement fund at the end of the year. The fund earns 11% per year. You will invest X dollars into the fund. You plan to retire at the end of 40 years from now. Once you retire, you will take your entire retirement fund and transfer it into a safer investment that will only earn 5% interest per year compounded monthly. You will need $4000 per month for 30 years during your retirement to sustain your lifestyle. (After which point, RIP). Calculate exactly how much money you will deposit in your retirement account at the end of this year. Your cousin who is the same age as you and with the same life expectancy and desired retirement age decides she will wait 10 years to start saving for retirement (so she will save for only 30 years). How much does she need to invest per year to achieve the same retirement nest egg as you when she retires? Finally, your lazy best friend who is also your age decides he will wait 10 years to start saving for retirement just like your cousin. However, he will only save the same amount you save per year. He will retire at the same time as you and reinvest just like you do into a safer investment. He will try to live the same life style as you. How long after retirement (in months) before he is broke?

Answer 1

1). Amount needed in the retirement fund at the time of retirement, to sustain $4,000 per month for 30 years:

PMT = 4,000; N = 30*12 = 360; monthly rate (or I/YR) =5%/12 = 0.417%, CPT PV.

PV = 745,126.47

You will need a corpus of 745,126.47 at the time of retirement.

The annual deposits you need to make for 40 years: N = 39; annual rate = 11%; FV = 745,126.47; PV = 0, CPT PMT.

PMT = 1,280.67 (Annual amount to be put in the retirement fund)

2). Annual savings for the cousin:

FV = 745,126.47; N = 30; rate = 11% (assuming her retirement fund earns the same rate); PV = 0, CPT PMT.

PMT = 3,743.96 (Annual deposits to be made by her for 30 years.)

3). PMT = 1,280.67; N = 30; rate = 11%, PV = 0, CPT FV.

FV = 254,879.82 (He will have this much in this retirement fund, at the time of retirement.)

To calculate how many months, his retirement fund will last at $4,000 per month withdrawal at 5% compounded monthly:

PV = 254,879.82; rate = 5%/12 = 0.417%; PMT = -4,000, CPT NPER.

Nper = 74.21 months so he will be broke after 74.21 months.