Monday, September 15, 2008

Monthly Savings vs. Weekly

Currently our savings plan has us setting aside roughly 15% of our gross pay into a main account every week. The purpose of which is to build up a hefty emergency fund that can cover 8 months of living expenses. The account we use is the fee-free (for our purposes) PC Financial Intrest Plus savings account which gives 3.05% APY.

For this particular savings account, interest is paid at the end of every month based on your average balance for that month.

Since I am a spreadsheet whore, I wanted to determine what type of savings frequency for the average individual would yield the best return and how much the different scenarios varied. For the experiment, I am

Assume the following

1. Assume annual take home income of $30,000 (any number will work, this is the one I chose)

2. You get paid every two weeks (as per most payroll schemes) on Friday which works out to be $1153.85

Note that it doesn't really matter when you get paid (weekly or bi-weekly), rather it matters when you put the money in the savings account.

3. You wish to save 15% of your annual income (most people say you should do 10%, but more is better; $4500 in this case)

4. The frequency of your placing dollars into a savings account is the variable

You can either put the money in once a month (your first check of each month), every two weeks when you get paid, once a week, or once a day

4.5 Since you are getting paid every two weeks, why would you space the savings over two weeks? Maybe it's a comfort thing and you feel better having a higher balance in your checking account in case something happens. Why would you spread things over a daily period? You likely wouldn't but if you did then it would likely be for similar reasons. Note as well that for the weekly or daily cases, you could consider that a different pay scheme as well. Instead of getting paid every two weeks, you get paid every week or every day and deposit into the savings on that same pay schedule.

5. In each case the total amount put into the savings will be the same

6. The calculation is done for 2007 so your first paycheck is on January 5.

7. The savings account we look at pays 4% APR and pays interest monthly (for the difference between APR and APY, go here ). Interest is calculated on each day’s closing balance and is paid into your account monthly (on the last day of every month at 11:59 pm). I may be wrong, but I assume that this means a daily interest rate is applied to your balance and the daily amounts of interest are added up at the end of the month. This is the way I will apply interest in this experiment.

8. You create the account on January 1, 2007 and the balance starts at $0 and you will start saving with your first paycheck.

We are looking for the way that generates the most interest in an average sense. Meaning the average person will not do the most optimal scenario of putting 15% of total income into the account as soon as possible. This would entail putting 100% of their paycheck into the account until the $4500 is reached at the expense of all other bills. Once $4500 is in the savings, then no additional savings would be put in. Mathematically, this will generate the most interest, but is simply not feasible or desired for most people. This is where the personal in personal finance comes in. Most people would not want to devote nearly 4 entire paychecks to the savings account right off the bat. The reason most people would be uncomfortable is that it would mean bills and other expenses get put aside, which would cause stress and potential penalties in terms of late fees. Thus for this experiment, "reasonable" savings plans will be employed.

If you were to employ this "brute force" method, you will have your 15% annual savings on February 16, 2007 with $115.40 left over to start paying bills. For me, this isn't worth the undue stress, but your mileage may vary. However, for completeness, I will look at some special cases: the brute force method of putting 100% of your paycheck away until your goal is reached, getting paid on the first of every month and making a deposit then, and depositing every day of the year rather than miss out on the first 4 days of 2007 waiting for the first paycheck.

In the case of putting money in monthly, you will put in $375 from the first paycheck of every month. This means that for the some months you won't be putting in the $375 till sometime mid-month.

In the case of putting money in bi-weekly (ie. every time you are paid), you will put $173.08 into the savings from each paycheck.

In the case of weekly, you break your savings contribution from your paycheck into two and in the case of daily you spread the contribution over two weeks. With the daily example, you miss out on the first 4 days of the year, but for your daily savings, you just divide $4500 by 361 instead of 365 to get $12.46/day.

Which plan will emerge the victor? Read and find out. You can download the spreadsheet with all the calculations here.

First Paycheck of the month used for savings: $4594.03. Total Interest: $94.03

Every Paycheck or Biweekly: $4591.14. Total Interest $91.14

Weekly: $4589.41. Total Interest: $89.41

Daily starting on first paycheck of 2007, Jan 5: $4588.67. Total Interest: $88.67

Daily starting on January 1, 2007: $4589.66. Total Interest: $89.66

Brute Force method: $4662.58. Total Interest: $162.58

Depositing on the 1st of every month: $4597.31. Total Interest: 97.31

So obviously the Brute force method will get you more interest, but as I mentioned above, the way to do so would likely not be worth it for most people. As for the other methods the differences aren't huge.

A few things I found interesting was that a difference of 4 days on a daily deposit schedule net's you another buck and getting your money in on the 1st of every month scores an extra 3 bones rather than waiting for the first check of the month.

So why does this happen? All it is, is the situation that if you have your money in earlier for interest to accumulate on, you will have more in the end. In terms of a bigger picture though, think about what type of savings plan works for you in whatever employment situation you're in.

1 comment:

schaef said...

Although this is unrelated to the post, I wanted to mention it before I forget:

Despite not giving a unit cost for everything purchased ($/kg, etc.), it does give a detailed review of each and every product payed for. Have a look-see!