# 3.1 Sums & Products

## 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.

Exercise 1

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.