How I Organize My Money - Debugging CD

CD (Certificate of Deposit) normally offers higher interest rate than the saving and money market accounts, but it requires you cannot withdraw the money for a specified period of time (for example: 6 months, 12 months, some CD has 60 months term). With the spike of the federal fund rate target, there are some CDs with 5% or more APY (Annual Percentage Yield). I recently bought some CD with 11-month term and 5% APY. I discovered various interesting things that I had not considered them before.

Firstly, I received my first interest after one month. The amount is lower than my expectation. ($37.5 of $10,000 5% APY CD). $10,000 * 5% / 12 months = $41.67 per month, not $37.5. Now you must think: “It’s the compounding, stupid.” Sure, let’s calculate with compound interest:

(1 + x) ^ 12 = 1.05, calculator says x = 0.004074, then, $10,000 * 0.004074 = $40.74, still not $37.5

Why?! Maybe it’s not compound by month but by day? So, I changed the calculation:

(1 + x) ^ 365 = 1.05, calculator says x = 0.00013368, then, $10,000 * (1.00013368) ^ 30 = $40.18, closer but still not $37.5

OK, I realized I bought the CD in Feb 2023, so, there are only 28 days.

$10,000 * (1.00013368) ^ 28 = $37.5. Yay!!

Compounding by day causes several subtle things to notice:

• If you buy $10,000 11-month 5% APY CD in February, you earn $456.51 total interests, but if you buy in March, you earn %460.62 total interests, because March has 3 more days than February.
• Because of compounding, the interest of the last month is noticeably more than the first month (roughly $42 compared to $37.5). That’s maybe why for higher interest rate, the bank offers shorter term like 11-month.

So, for the unique term of 11-month CD, buy in March is better than buy in February. Also, for the same APY, the longer the term, the bigger the difference due to compounding. To conclude, it’s the power of compounding. The power of long term.