Jake B. answered • 06/02/20

Experienced Finance and Guitar Tutor

Hi Leslie,

The easiest way to solve this problem is with a financial calulator. We need to figure out the values to plug in for n (# of periods), i (interest), PV (present value), PMT (payment), and FV (future value). We are given a PV of $300,000 which is the amount we have today. We must solve for PMT in order to determine the amount of money we can withdraw each period for retirement.

A common mistake is to plug in 5% for i and 20 years for n, but here's the catch: ** interest is compounded monthly**, and therefore we must take that into account when determining the input values. For instance, there are 12 months per year which means that there are 20 yrs x 12 months = 240 periods total for the life of this problem. Therefore 240 is our "n" value, not 20.

Next, let's look at i: we have a rate of 5% per year, but we are speaking in terms of months – so what rate do we use? We must divide 5% by 12 to get a monthly rate of about 0.417%.

Finally, we look at FV: We must find the amount of money we have at the end of 20 years, or 240 months. This problem assumes that we use up all funds by the end, so FV = 0.

__Summary:__

*PV = -300,000

n = 240

i = 0.417%

FV = 0

PMT = ?

*Note how I entered PV with a negative sign. The general convention is to treat PV as a "cash outflow." Financial calculators will require that there is an input entered as negative to make everything balance. In this case, entering a positive PV would have made the calculator output a negative "PMT."

Solving for PMT will result in an answer of $1,979.87 which is the amount we can withdraw each period.

I hope this helped!