How Much Do I Need To Invest To Save $X?

Monday I discussed the future value of money, given a known principal, interest and time.  This is all well and good, but what happens if you want to have a certain amount within a specified time at a known interest?

For today, we'll say that you want to have a $5,000 emergency fund in 18 months and you will be putting the money into a savings account earning 5%.

Now, just like Monday, you have the same two options, either put the initial principal in once, or add it as an annuity.

For a single deposit, use this equation:

For an annuity, use this equation:

So, how much do we have to put in to achieve our goal?

For a single deposit, we need to deposit only $4639.44, but for an annuity, we'd have to deposit $268.07 per month for a grand total of $4,825.25.

At this point, we've investigated the future value of money in terms of a fixed total going in, and a fixed future value.  It would appear from these two cases that annuities are a weaker choice given a fixed period and rate for both a fixed input and a fixed output, but what about when period or rate becomes the variable?  

We shall see what happens with these two as variables in the next two posts (tomorrow and Friday), finishing up the week (Saturday) with a complex example.