Is there a neater strategy to clear up the next while not having to calculate each time period ?

Adam lives in a rustic the place there is no such thing as a earnings tax. The annual charge of inflation on this nation is 6%. The banks of this nation give 5% curiosity annually. The charge of inflation and the financial institution rate of interest won’t ever change.

He is about to obtain an inheritance and he desires to get simply sufficient cash that may final him precisely 30 years. He plans on depositing this quantity within the financial institution and get the 5% curiosity annually.

Adam has a yearly expense of 4402000 which he withdraws originally of every yr. His yearly bills will improve with inflation i.e his bills will improve by 6% annually. Assuming that Adam can have no different supply of earnings, what actual quantity does he want from his inheritance ?

For instance, that is how a lot Adam might be left with after 2 years.

Let us assume that Adam obtained y quantity as inheritance. Let x= 4402000.

Amount Adam has on the finish of the first yr = (y-x)*1.05

Amount Adam has on the finish of the 2nd yr

= ((y-x) * 1.05-x * 1.06) * 1.05

= y* $1.05^2$ -x*$1.05^2$ -x * 1.06*1.05

Now, I can write down each time period and clear up this. And it won’t take an excessive amount of time both. But, if as an alternative of 30 years, we had been to calculate the inheritance quantity for , say, 1000 years then we’d not have the ability to take action. What is a wiser means of fixing this ?