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.
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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+R)^-N)/(R)]+FV*(1+(R))^-N+PV=0
-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.
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