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

My plan:

I am confused with fist question (Whether my retirement plan is lump saving or per year saving). Because there is not mention any per year saving for my plan. But later one, when my friend's plan come he is saving as my plan per year. SO, I am using both option here:

Particular	Data	Formula
PMT in retirement age per month	4000	Given
Return from investment per month	5%	Given
During of retirement in month	360	30*12
Requirement amount at retirement time	80000.00	Pv formula in excel

So, If I am saving lump sum basis (One time saving):

Particular		Formula
Return	11%	Given
Year of saving	40	Given
Needed Amount after 40 years for retirement	80000	Calculated above
Today's Lump sum Amount for retirement	1230.75	PV formula in excel

Conclusion: Lump sum investment of $1230.75 will become $80000 after 40 years with 11% return. And that corpus will provides 4000 $ per months for retirement period (30 more years).

So, If I am saving per year basis :

Particular		Formula
Return	11%	GIven
Year of saving	40	Given
Needed Amount after 40 years for retirement	80000	Calculated above In my plan
Today's per year Amount saving for retirement	137.50	PMT formula inn excel

Next,

My cousin Plan

Particular		Formula
Return	11%	Given
Year of saving	30	Given
Needed Amount after 40 years for retirement	80000	Calculated above In my plan
Today's per year Amount saving for retirement	401.97	PMT formula in excel

$ 401.97 per year saving will provides her $80000 corpus after 30 years. And as my plan, that 80000 $ will survive the rest retirement life.

My friend Plan:

Particular		Formula
Return	11%	GIven
Year of saving	30	Given
Needed Amount after 40 years for retirement	27365.37	FV Formula in excel
Today's per year Amount saving for retirement	137.50	Calculated in my plan

His total generated amount in these 30 years is 27365.37 $

I don't find an exact formula for this, So, I have calculated it with using some logic here:

Total Saving	27365.37	Given
Return Rate	5%	Given
Monthly Expenses	4000.000	Mentioned in question
Percentage of expenses	14.617%	Total Saving/Monthly Exp. (In percentage form)
Effective Expenses Rate	9.617%	14.617%-5% (Actual Expenses Percent)
Actually expenses in month	2631.731464
Sustainable month	10.39823823	Total Saving amount/Actual expenses in month