# Checking The Math On My Ally CD Interest

I blogged about my experience with closing an Ally CD account a while ago. But as I was writing that post, I found that I had a hard time reproducing the numbers on my statements.

Here are the facts:

• 4/9/2013 – I deposited $7,000 into an Ally CD account • 12/31/2013 – Interest paid in 2013 is$55.73 per the 2013 1099-INT
• 4/21/2013 – I closed my account. Per the April statement the interest paid in 2014 is $23.09, and the early withdrawal penalty is$12.57.
• The annual percentage yield is 1.09%

Total interest paid is $55.73+$23.09 = $78.82 First, let’s check the math on my 1099-INT. I am using this formula: $A(t) =A_0(1+\frac{r}{n})^{nt}$ Where: $A_0$ = principal amount $t$ = time period the intial amount is deposited for in years $n$ = number of times the interest is compounded per year $r$ = annual interest rate $A(t)$ = total amount accumulated after t years The principal amount is $A_0$ =$7,000 and the interest is compounded daily, $n$ = 365. Assume that the interest earned during the day is credited at 0:00am the next day. Then interest is compounded 266 times in 2013 from 4/9/2013 to 12/31/2013. So we have:

$A(266)=\7,000(1+\frac{1.09\%}{365})^{(365)(\frac{267}{365})}=\7,055.83$

So, should the interest for 2013 be $55.83 instead of$55.73? But wait, the $7,000 was not in the account for the entire day on 4/09/2013. I check my account activity and it turns out that I transferred the money into my CD at 11:59am. On 4/09/2013 only$7,000 x 1.09% x (0.5/365) ~ $0.1045 of interest is earned. Using $A_0 = A_1$=$7,000 x 1.09% x (0.5/365) , the total amount from 4/09/2013 to 12/31/2013 comes out to be:

$A(265)=A_1(1+\frac{1.09\%}{365})^{(365)(\frac{265}{365})}=\7,055.72$

Okay, much better. Now it is only off by only 1¢, which is probably due to rounding error.

Let’s apply this to 2014. I am going to use $A_0 = A_2$ = $7,055.73 as the principal amount. Interest is compounded 110 times from 1/1/2014 to 4/21/2014: $A(110)=A_2(1+\frac{1.09\%}{365})^{(365)(\frac{110}{365})}=\7,078.95$ There is a difference of 13¢ when compared with the statement amount of$78.82. I am already assuming that no interest is earned on 4/21, the day that I called customer service, but somehow my number is still more than the one on the statement.

What about the penalty? It doesn’t seem like the penalty is the interest that I earned in the last 60 days:

Using $A_0= A_2 =\7,055.73$

$A(110) - A(50) = \12.68$

The penalty is closer to the first 60 days of interest had the initial deposited amount been in the account for a full 60 days.

$A(60) -\7,000 =\7,000(1+\frac{1.09\%}{365})^{(365)(\frac{60}{365})}=\12.55$

But my calculation is still off, this time by 2¢.

I am really bothered by the fact that I cannot arrive at the exact amount on the 1099-INT and on the April bank statement. All my calculated numbers are a couple pennies off. I am not sure if it is due to rounding error or if my math is incorrect.

If you are not interested in checking my calculation, it is still a fun exercise to check the math on the interest in your own online banking account. Let me know what you find out!