Hello, good folks. I'm a retired senior citizen that needs some help. I recently retired and have a retirement account of about $750,000. I wish to receive annual annuity payments for 20 years. I'm reliably told that I can get 7% on my investment. Here is my question: I wish to withdraw money from my account, for my livings expenses, but I also would like to leave $250,000 for my two grandchildren, roughly 5 years after I receive my 20th and last payment when they will be in their thirties. Can you folks figure out how much would my annual payments be and still allow me to leave enough money to grow to $250,000 at 7% for my two grandkids? Any help would be appreciated and I thank you.

Guest May 28, 2017


Where do you get 7%?  If they said that, it's a floating rate. Typical BS from investment advisors.  

Guest May 28, 2017

You are possibly right! But, let us use it as the theoretical number to calculate the payments. In fact, my retirement account is mostly in "balanced mutual fund", which has averaged better than 7% in the last 10 years.

Guest May 28, 2017

First, we have to determine how much money you should leave after your 20th and last payment. Since we know you want it to grow to $250,000 in 5 years' time, then we can easily figure its PV at the end of your last payment. Will use this common formula to do that:
PV = FV x [1 + R]^-N
PV =250,000 x [1+0.07]^-5
PV =250,000 x 0.7129862......
PV = $178,246.54 - this is the amount you must leave, which will grow to $250,000 at the assumed rate of 7%.
Now, how do we figure out your annual payments and still leave this amount we just calculated? There are a couple of ways of figuring that out:
1- We can calculate the Future Value of your $750,000 investment @ 7% over a period of 20 years, which comes to =$2,902,263.35.
2- From this amount we have to subtract the amount you wish to leave for your grandchildren =$2,902,263.35 - $178,246.54 = $2,724,016.81. This is the Future Value of your 20 annual payments.
3- Now, we can easily figure out your annual payments by using this financial formula:
FV=P{[1 + R]^N - 1/ R}
2,724,016.81 = P x {1.07^20 - 1 / 0.07}
2,724,016.81 = P x  40.99549........
P =2,724,016.81 / 40.99549......
P = $66,446.74 - This is your expected annual payment @ 7% for 20 years.
We can also figure out your annual payment in another way just to make sure that the whole thing is accurate. We can use a more complicated-looking formula to give us the annual payments directly. And that formula looks like this:
-P*[(1-(1.07)^-20) /(0.07)] - 178,246.54*(1.07)^-20 + 750,000 = 0
-P*10.594014245...  - 46,062.29 + 750,000 = 0
-P*10.594014245 = -703,937.71
P = -703,937.71 / - 10.594014245
P = $66,446.74 - Which is the same as the above annual payment.

Guest May 28, 2017

Thank you very much for this. I don't think I can understand the math, but thanks again.

Guest May 28, 2017

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