Exercise

# Diminishing cash flows

Remember how compounded returns grow rapidly over time? Well, it works in the reverse, too. Compounded discount factors over time will quickly shrink a number towards zero.

For example, $100 at a 3% annual discount for 1 year is still worth roughly $97.08:

\( \frac{\text{Value}}{(1 + \text{Discount Rate} )^{\text{# of Discount Periods}}} = \frac{\text{\$100}}{(1 + 0.03)^1} = \text{ \$97.08 } \)

But this number shrinks quite rapidly as the number of discounting periods increases:

\( \frac{\text{\$100}}{(1 + 0.03)^5} = \text{ \$86.26 } \)

\( \frac{\text{\$100}}{(1 + 0.03)^{10}} = \text{ \$74.41 } \)

This means that the longer in the future your cash flows will be received (or paid), the close to 0 that number will be.

Instructions

**100 XP**

- Calculate the present value of a single $100 payment received 30 years from now with an annual inflation rate of 3%, and assign it to
`investment_1`

. - Calculate the present value of the same payment, but if it was received 50 and 100 years from now, and assign it to
`investment_2`

and`investment_3`

respectively.