## Annuities

Assuming you could be sure of getting a 4% return forever on the money you invest, what would be a proper amount to invest now for an annuity that would pay you $10,000 yearly forever starting a year from now?

Enter the whole dollar amount without commas or the dollar sign. For example, if you want to invest $140,000.00, you should type 140000.

The current value of $10,000 paid out \(i\) years from now is \(\frac{10,000}{1.04^i}\). Summing this for \(i=1,2,\ldots\) we get $250,000.

Alternatively, putting $250,000 in the bank today will allow us to collect 0.04\(\cdot\)$250,000 = $10,000 every year, starting a year from now.