Calculated CD Maturity Value Higher than Deposited

[frice]

Hi, could you please verify or correct how I am going about this?

18 months ago I opened a $100,000 18 month CD at 5.00% APY, 4.94% Dividend Rate. The agreement states Dividend Payment Frequency: semi-annually and Payment Method: compound. The rates (advertisement) sheet I read in 2023 and the one they post now both state Compounding and Crediting Frequency: semi-annually for their 18 mo CD. This CD recently matured and the end result was less earnings than I had calculated. I called the bank and was told little of value. "They'll look into it".

An online interest calculator set to semi-annual compounding spit out $7594.53 of final earnings.

In manually calculating this in 2023 and now, I factored in two "compounding events" at 12 months and 18 months. By this I mean that at 6 months the dividend would be based on my initial investment so the 6 month dividend wouldn't benefit from a "compound event". Using the annual dividend rate of 4.94% I figured that each of the three dividends would be:
$2470.00
$2531.00
$2593.52
...for a total of $7594.52 in earnings. $0.01 off of the internet calculator, a rounding error. My actual deposited earnings were reported as $7558.99. It's only $35 less, but I DID select this CD based on advertised compounding and would expect to receive it. Their total appears to involve almost no compounding at all, or some sort of rate change occurred (supposed to be fixed), or it involves some daily calculation gymnastics I'm not privy to.

About the only bit of info I got from my phone call was they use 545 days for the 18 month period. 547.5 days would be the exact half of 1.5 (365 day) years, but this is splitting hairs. 2.5 days doesn't make a $35 difference.

Am I doing something wrong? Or is there something in the legal details or standard bank operating procedure I'm missing?

[jeffyscott]

With a balance of about $107,500, the few days do seem to be sufficient to account for $35.

107,500 X .0494 / 365 = $14.55 per day.

For the last interest payment use .0494 x 180 ÷ 365 to calculate the interest and it's $2558.

[#Cruncher]

18 months ago I opened a $100,000 18 month CD at 5.00% APY, 4.94% Dividend Rate. ... An online interest calculator set to semi-annual compounding spit out $7594.53 of final earnings. ... My actual deposited earnings were reported as $7558.99. It's only $35 less, ... they use 545 days for the 18 month period. 547.5 days would be the exact half of 1.5 (365 day) years, but this is splitting hairs. 2.5 days doesn't make a $35 difference. (highlighting and underlining added)

With a balance of about $107,500, the few days do seem to be sufficient to account for $35.

Indeed. The 2-1/2 days do account for the difference to within a couple of cents.

Code: Select all

Start                100,000.00 	
Grows to in  6 mo    102,470.00 = 100000    * 1.0247
Grows to in 12 mo    105,001.01 = 102470    * 1.0247
Grows to in 18 mo    107,559.01 = 105001.01 * (1 + 0.0247 * (180 / 182.5))
Gain per bank          7,559.01 = 107559.01 - 100000

2-1/2 days interest       35.53 = 105001.01 * 0.0247 * (2.5 / 182.5)
Gain per internet      7,594.53 = 100000    * (1.0247 ^ 3 - 1)

Notes

• it looks like the bank rounds the "Dividend Rate" to two percentage places when converting from the 5% Annual Percentage Yield (APY):
  2 * (1.05 ^ 0.5 - 1) = 4.939% ==> 4.94%
  So the 6 month rate it uses is exactly half of 4.94% or 2.47%.
• If the CD term was a full 18 months, only giving you a fraction (180 / 182.5) of the interest for the last six-month period does seem like a cheap trick. Do you have the exact inception and maturity dates for the CD?

[frice]

With a balance of about $107,500, the few days do seem to be sufficient to account for $35.

107,500 X .0494 / 365 = $14.55 per day.

For the last interest payment use .0494 x 180 ÷ 365 to calculate the interest and it's $2558.

Thank you, jeffyscott. I mostly understand what you are saying in terms of a daily calculation. My (inexperienced) understanding of the terms is that the CD would calculate a dividend once every 6 months. Quoting my original post: "The agreement states Dividend Payment Frequency: semi-annually and Payment Method: compound. The rates (advertisement) sheet I read in 2023 and the one they post now both state Compounding and Crediting Frequency: semi-annually for their 18 mo CD."

If I had gone into this thinking they credited daily I would have figured the ~$35 difference was due to 2.5 days less than "exactly 1.5 * 365 days".

Is there another rule that wasn't listed, or should a consumer understand that the rules they listed really mean daily average * some unwritten number of days? Is 545 days the standard for an 18 month period?

[jeffyscott]

Don't know the answers to either of those questions but you can't expect to earn interest for more time than the actual duration of the CD. It was apparently a 545 day CD (nominally called 18 months by the bank) and the interest was added to the balance at 6 months, 12 months, and 545 days. So assuming the actual maturity date was 545 days from the start date, you were paid the promised yield.

Calling it 18 month is similar to referring to the 52 week t-bill as 1 year, 4 week as 1 month, etc.

[frice]

18 months ago I opened a $100,000 18 month CD at 5.00% APY, 4.94% Dividend Rate. ... An online interest calculator set to semi-annual compounding spit out $7594.53 of final earnings. ... My actual deposited earnings were reported as $7558.99. It's only $35 less, ... they use 545 days for the 18 month period. 547.5 days would be the exact half of 1.5 (365 day) years, but this is splitting hairs. 2.5 days doesn't make a $35 difference. (highlighting and underlining added)

With a balance of about $107,500, the few days do seem to be sufficient to account for $35.

Indeed. The 2-1/2 days do account for the difference to within a couple of cents.

Code: Select all

Start                100,000.00 	
Grows to in  6 mo    102,470.00 = 100000    * 1.0247
Grows to in 12 mo    105,001.01 = 102470    * 1.0247
Grows to in 18 mo    107,559.01 = 105001.01 * (1 + 0.0247 * (180 / 182.5))
Gain per bank          7,559.01 = 107559.01 - 100000

2-1/2 days interest       35.53 = 105001.01 * 0.0247 * (2.5 / 182.5)
Gain per internet      7,594.53 = 100000    * (1.0247 ^ 3 - 1)

Notes

• it looks like the bank rounds the "Dividend Rate" to two percentage places when converting from the 5% Annual Percentage Yield (APY):
  2 * (1.05 ^ 0.5 - 1) = 4.939% ==> 4.94%
  So the 6 month rate it uses is exactly half of 4.94% or 2.47%.
• If the CD term was a full 18 months, only giving you a fraction (180 / 182.5) of the interest for the last six-month period does seem like a cheap trick. Do you have the exact inception and maturity dates for the CD?

Thanks, #Cruncher. Inception date 9/1/23, maturity 2/27/25.

You and jeffyscott have given me the info to look further. I calculated out the three dividends based on number of days within each period. Using a calendar calculator for accuracy, the three periods contained the following number of days:
182
184 (includes a leap day)
179

I then calculated payments again using these #ofday values/182.5 as a "corrected 6 month" factor. I was $0.17 off in total of what the bank deposited so I must have missed some minute consideration, but it is clear this is how they figured their payments.

Then I found some boilerplate CD info from the bank that wasn't on the account agreement or advertising copy. "Dividends are calculated by the daily balance method which applies a daily periodic rate to the balance in the account each day". I have found no written mention of using 180 days (or 179 days in my case, or 545 total days for an 18 month term as the CS stated) as their calculation method. But the math checks out. I had thought the wording I posted from their agreement suggests the payments were 6 month lump calculations, not figured and portioned daily. I suppose this is normal practice but it seems disingenuous.

All of this is an exercise to learn more about investing; the $35 is a drop in the bucket. It did shock me initially due to there only being $9 more earnings than had it been a 547.5 day 18 month period at 5% without compounding. I railed on the wrong issue in an attempt to figure out why the difference existed. Thanks again.

[frice]

Don't know the answers to either of those questions but you can't expect to earn interest for more time than the actual duration of the CD. It was apparently a 545 day CD (nominally called 18 months by the bank) and the interest was added to the balance at 6 months, 12 months, and 545 days. So assuming the actual maturity date was 545 days from the start date, you were paid the promised yield.

Calling it 18 month is similar to referring to the 52 week t-bill as 1 year, 4 week as 1 month, etc.

Yes, I'm learning this. I trusted the 18 months to mean 1.5 * one calendar year. The agreement wording didn't help my understanding about daily average and the way it is implemented. I have since found some boilerplate from the bank concerning CDs in general: "Dividends are calculated by the daily balance method which applies a daily periodic rate to the balance in the account each day". Live and learn, thanks to your help.

[jeffyscott]

I think it's normal that interest is accrued daily (or maybe "nightly" would be more accurate ) and then actually paid (added to the CD balance) periodically. Some pay that out monthly, some quarterly, and yours was semi annually. Of course, the final interest payment will be at maturity and will be whatever has accrued since the last interest payment.

I imagine they're using 30 days = 1 month for under a year and 365 days for a year. So 365 + 30 x 6 is where the 545 comes from.

[rossington]

Don't know the answers to either of those questions but you can't expect to earn interest for more time than the actual duration of the CD. It was apparently a 545 day CD (nominally called 18 months by the bank) and the interest was added to the balance at 6 months, 12 months, and 545 days. So assuming the actual maturity date was 545 days from the start date, you were paid the promised yield.

Calling it 18 month is similar to referring to the 52 week t-bill as 1 year, 4 week as 1 month, etc.

Yes, I'm learning this. I trusted the 18 months to mean 1.5 * one calendar year. The agreement wording didn't help my understanding about daily average and the way it is implemented. I have since found some boilerplate from the bank concerning CDs in general: "Dividends are calculated by the daily balance method which applies a daily periodic rate to the balance in the account each day". Live and learn, thanks to your help.

Hi OP,
Didn’t your original contract state the amount of the ending balance at maturity?
Also they do specifically use the actual calendar days within the term of the CD to calculate.

[Itzapi]

Banks use daily interest computations before making interest credits according to predetermined schedules. The terms disparity of 545 days between your bank and the labeled time period generates the $35 difference in the interest amount. Your interest payment corresponds to the promised yield although the bank distributes the interest pro-rata manner.

[InvestSage]

Let's start with this... honestly... It seems like you've done a thorough job calculating your CD earnings.

The slight discrepancy could be due to the bank's specific compunding method or a minor difference in the number of days used for the calculation. Banks sometimes use different day-count conventions, which can affect the final amount.

It's also possible that there were minor fees or adjustments not clearly statd.