Pay Off Debt: Calculate Interest & Time Needed for Snowball Method

[Cwray]

I'm starting a "debt snowball" approach to paying off my debts and am wondering how long it will take to pay them off and how much interest I will end up paying annually. I'm ok with math, but this is too complex for me.

I have:
3 credit cards
car loan
personal loan
401(k) loan

If someone is willing to help me figure it out, that would be great and then I'll give all the specific information. Thanks!

 

[Ackbach]

Paying off your debts is a fantastic thing to do, and I would give you a hearty back slap to encourage you in that process.

To find out how long it will take to pay off any single debt, you must assemble the following information:

1. Principle - this is the amount of the original loan
2. Interest rate
3. Compounding Interval - this is how often the interest is incorporated back into the principle

Once you have all this, the formula for computing how much the loan is worth is given by
$$S=P \left(1+\frac{j}{m} \right)^{\!mt},$$
where
\begin{align*}
S&=\text{value after }m\text{ periods} \\
P&=\text{principle} \\
j&=\text{interest rate} \\
m&=\text{number of times interest is compounded per year} \\
t&=\text{time in years}
\end{align*}
In this formula there is no hint of your payment. How do we put that into the mix? Well, suppose your monthly payment is $b$. Then the amount of money you've paid off at time $t$ is given by $bmt$. This is assuming your payments coincide with the compounding periods. To find out when you will pay back the debt, solve the equation
$$bmt=P \left(1+\frac{j}{m} \right)^{\!mt}$$
for $t$. This is a transcendental equation, and not easily solved. However, you can solve it in terms of the Lambert W, or product log function. WolframAlpha gives the solution
$$t=-\frac{W\left( -\frac{\ln\left(P\left(\frac{j+m}{m}\right)\right)}{b}\right)}{m\ln\left(P\left(\frac{j+m}{m}\right)\right)}.$$
But this is more complicated than you need. I would just whip up an Excel spreadsheet, and play around with both sides of the above equation until you get the LHS to be greater than the RHS. That will be the time when you pay off the loan.