Rate 9%,I will be making 30 annual payments so that in 30 yrs I want to receive 80,000 a year.What is the pmt?

Question

You are helping your friend to plan retirement. She thinks that she needs 80,000 a year starting from her 66th birthday. Now she just celebrated her 35th birthday. She plans to make an contribution to her retirement account every year starting from her 36th birthday and she plans to make the same contribution till she is 65 (altogether 30 contributions). If the retirement account earns 9% per year, what does her annual contribution need to be?

Answer 1

You left out a couple of key points. How long does she expect to live? Forever? What is the forecast inflation rate? Will she have to pay taxes on the earnings in her account?

Lets assume 0 inflation and that she does plan to live for ever. No taxes will be paid. Makes it real easy.

She will then require a sum of $888,888.89 on her 66th birth day.

She will no longer be contributing after her 65th birth day. So she will require $815,494.39 on her 65th birthday. Her multiplication factor is 136.3075385. So she needs to contribute $5982.76 annually, if my calculations are correct.

Answer 2

You have to start at the end, and work backward from death to age 35. Does she need $80,000 a year at retirement in perpetuity, without reducing the principal? Or can she reduce principal so that she has nothing left at the end of her expected lifetime? If so, what is her expected lifetime, i.e., expected years in retirement. For example, if she retires at 65 and lives to 95, she'd have 30 years of retirement.

Since we aren't given an expected lifetime, I'm going with the first assumption - she'll get $80M per year without reducing principal. In that case, she'll need $968,888.89 at retirement age of 65. Use a financial calculator to solve for present value to get this number (i=9%, pmt=$80,000, n= infinity). Then take the same number, using it as the future value, and solve for payment (FV=$968,888, PV=$0, i=9%, n=30). You're now using this as a future value because you now know that this is the amount you need at age 65 after 30 years of payments. So the answer to your question is that annual payments of $6,521 will be needed.

You can check this by plugging it all back in. If you contribute $6,521 per year for 30 years at 9%, you'll have $968,888 at retirement. Then, at that point you can withdraw $80,000 in perpetuity without reducing principal (($968,888 - $80,000)*1.09 = $968,888). Run the numbers and check it out - good luck.

Answer 3

Don't forget about inflation. 80,000 30 years from now will probably be like 40,000 today. Assuming a 2.5% annual inflation rate to have 80,000 in purchasing power in 30 years will require 167,000.
However, with a 9% retirement account that should be easy enough to do - she has plenty of time.

Assuming she lives to be 90 she will need 80,000 per year (adjusted for inflation each year) for 25 years. That is quite a bit of money but very doable. She will need 167,000 the year she turns 66 and 311,000 the year she turns 90. (you have to continue to consider inflation after retirement). Acounting for all the years inbetween she expects to need a total of 5,875,000. However she doesn't need all of that when she turns 65 (since her money will still be collecting interest).

By my very rough calculations (in excel) she needs right around 2,100,000 at retirement. This will provide enough of a lump sum to collect 9% interest while removing 167k annually (adjusted for inflation each year)

To save 2,100,000 in 30 years you need to put away about 16,000 a year (at 9%). However, I am assuming she saves the same amount each year, with inflation/age comes more money in salary each year that means you could contribute less now and catch up later because your income will be much higher. Assuming salary goes up by 2.5% a year (same as inflation) she could get away with putting away 12,500 at 36 and increasing her contribution by 2.5% each year (12,800 at 37, 13,100 at 38, etc...). Stopping at 25,500 at 64.

Hope that helps, she should consider consulting a financial adviser for much more accurate numbers. Get recommendations from friends and family though and don't get caught up in any crazy Universal life policies - most of the money should be in mutual funds and bonds (adjusted accordingly to take risk/return into account)

Good luck

Answer 4

Well let's say you'll live till 90 yrs old tops, so you got 25 years (90-65) spending $80K/year. That comes to about $2M.
That means that at age 65 you'll need about $2M. If you consider that you will probably receive some interest during those 25 yrs on this amount at age 65 all you really need is about $1.9M (based on the assumption that you will be making about 6% interest on that amount during retirement. If you think you can invest for higher than 6% then you will need less than 1.9M to start retirement) The payment/year you need to make to have 1.9M at age 65 comes to about $57K($4,725/month).
If you change any of the assumptions you can always go to http://www.investopedia.com/calculator/ and recalc.

Answer 5

assuming you want a lump sum at the end of 30 years of $80,000, I think the formula to use is:

A = F * [ i / ((1+i)^(n-1))]

So
A=80000 * [.09 / (1.09^29)]
A = annual amount = ~592 dollars annually would give you 1 future lump sum equal to $80,000 in 30 years

If you want annual payments of $80,000 starting in 30 years, i think you need to know how long you want those payments to last.