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I'm trying to create a certificate of deposit (CD) comparison tool and have been working on a formula to compare a CD with a higher interest rate to a CD I might own with a penalty period. I believe the basic formula idea:

CD Comparison

Where:

  • FVc = Future Value of current CD
  • CVc = Current Value of current CD (Today's value with penalty)
  • rn = The new CD's APR
  • npern = The new CD's compounding frequency
  • nm - nt = Periods till maturity minus periods passed as of today. (The number of periods left till maturity)

This formula simplifies to:

Simplified CD Formula

Where:

  • rn/rc= The new/current APR
  • npern/nperc = The new/current compounding frequency
  • nm - nt + np = The periods till maturity minus the periods passed today plus the penalty periods of the current CD.
  • nm - nt = The periods till maturity minus the periods passed today of the new CD.

My question is this: This looks suspiciously close to the formula for compounding basis conversion formula at Wikipedia and copied below. Can anyone help me understand the relationship between these two calculations? Additionally, is my formulation correct?

Compounding basis

To convert an interest rate from one compounding basis to another compounding basis, the following formula applies:

Compounding Basis

where r1 is the stated interest rate with compounding frequency n1 and r2 is the stated interest rate with compounding frequency n2.

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    Wow. That's a lot of equation for a simple concept. How about "calculate the value of current CD to maturity, then calculate the value you'd have at the same time (as the maturity) after penalty but adding new interest until then.... The math appears pretty straightforward. – JTP - Apologise to Monica Jun 15 '12 at 0:13
  • I've done the one off calculations often but for instance, that calculation doesn't tell me what rates I should be looking for. Additionally the ideal rates are dependent on the day so a graph is usually more helpful.For example, plugging in the formula into Wolfram Alpha shows me that at day 50 with a 90 day CD that pays 0.39%, I need somewhere close to 1.00% for the switch to make sense. Assuming of course my calculations are correct :) – Cowlby Jun 15 '12 at 3:00
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    @Dilip - Not all banks impose a 3 month interest penalty for breaking a CD. For example, Ally Bank imposes a 60 day interest penalty and also offers no-penalty CDs (at a lower rate). – Greg Jun 15 '12 at 15:38
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    Unless you are re-inventing the wheel to create a competing product (and even if you are), why not check what your formula gives you against the first hit on Google when you search for "breaking a CD"? – Dilip Sarwate Jun 15 '12 at 16:00
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    "... but it is only useful in comparing CDs." Sorry, I misunderstood the purpose of your tool. It is the words in your first sentence "I'm trying to create a CD comparison tool" and subsequent repeated mention of CDs that is the cause of my confusion. – Dilip Sarwate Jun 15 '12 at 22:07
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My question is this: This looks suspiciously close to the formula for compounding basis conversion formula at Wikipedia and copied below. Can anyone help me understand the relationship between these two calculations? Additionally, is my formulation correct?

This should like the compounding basis conversion because essentially you are converting from rate 1 to rate 2 when you switch CDs. The equation should look similar because it is a very similar problem.

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Note that what many people do to limit the penalty for breaking a CD is to set up a series of CDs, dividing the lifetime of the CD between however many there are. For example, when I briefly had some of my money in 3-month CDs running (because I needed the cash available relatively quickly and the rate on even a 3-month CD was much better than on my savings account), I started three separate CDs in successive months, renewing each when its time was up. If I had needed to break into one prematurely, I could have picked the one which would minimize the amount of interest lost.

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