Situation:
Total Principal: 3,000,000.00
200,000.00 in 15 monthly equal installment at 10%
First (#1) due date is 7/5/08 until last (#15) due date is 9/5/09
#1 - 7/5/08 - 200,000.00, interest -25,095.89 - 458 days
#2 - 8/5/08 - 200,000.00 23,452.05 - 428 days
#3 - 9/5/08 - 200,000.00 21,753.42 - 397 days
...
...
...
...
#13 - 7/5/09 - 200,000.00 5,041.10 - 92 days
#14 - 8/5/09 - 200,000.00 3,397.26 - 62 days
#15 - 9/5/09 - 200,000.00 1,698.63 - 31 days

Total monthly installment due as of 9/5/09 - 3,000,000.00
Total interest due as of 9/5/09 - 200,767.12
Total due (principal + interest ) - 3,200,767.12

Daily interest - 54.79452

Can someone provide me a confirmation if my computation is correct or not.

Thank you.

First, check the background info (the discussion in your text, e.g.) to see if there's any particular 'day count convention' you're asked to use. If you're not told otherwise, use a simple 30/360 day count for situations like this--which just means that each month's interest will be 1/12 of a full year's interest. It looks like you're trying to assign specific day-counts to the months (30 days, 31 days), which is an admirable attempt at accuracy, but in most cases the markets have adopted simplified DC conventions, and textbooks usually follow that same idea.

The computations play out like this: Starting with a 3M amount, the first month's interest (which is due Jul 05 2008) is 3M x 10% / 12 = 25K. Therefore the first payment is paying 25K of interest expense, and the remainder of the payment (175K) pays down the principal.

Thus, immediately after the first payment the balance of the note is now 2.825M. That in turn means that the interest due with the second payment (Aug 05 2008) is 2.825M x 10% / 12 = 23,541.67. So if that much of the second 200K payment is going toward interest, that leaves 200K - 23,541.67 = 176,458.33 going toward balance pay-down. The result is that the note's balance is 2,648,541.67 immediately following the second payment.

Get the pattern? Finish up by continuing that sequence through to the 15th payment. Once you've completed your amortization schedule this way, you can determine the answers you need for your questions.

ArcSine - I'm reading this a bit differently. The 200,000 payments x 15 payments comes out exactly to the 3 million. Meaning the interest can't be included in those payments. There are loans that are an even principle amount plus the interest that would be due on that amount. i.e. first payment would be $25K of interest in addition to the $200K of principle payment. I don't see them in textbooks very often, but I've seen them in real work.

I am only deducing that since those payments can't include interest and then equal the principle. The only exception would be if that 3 million due in 15 months was actually discounted back to a present value first. For instance, purchasing something at an "unknown" price, but requiring a total of 3 million in payments, with an imputed interest rate, and then discounting back to a present value (cost of purchase) of 2,809,101.

Since the OP didn't include the instructions (hint, hint), it's impossible to know which. If the first senario, it would be correct (except for the questionable days).

Whaddya think?

Yep, I'd think the smart money says that you are spot-on, MG3. Giving it a second glance, it sure looks like OP was trying to describe a "even principal plus interest" type of amortization of that note, just as you've said.:o

So with every monthly payment the principal declines by 200K, and the total monthly payment is the sum of the 200K plus the interest for the given month.

I had "level payment with balloon after X payments" on the brain, and pulled the trigger too quick.

With OP's opening line about "total principal of 3M", and then the method OP used in the calcs, I'm inclined to think it's an "even principal plus interest" scenario, rather than "PV of 15 payments of 200K" kinduva thing.

I'd still advise Elacap to check the background info carefully re the day-count convention that might be prescribed in the text. Also, Elacap, the instructions underlying the problem would be helpful, since there's (as you can now surmise) a couple of different reasonable translations of your problem.

Thanks for the sharp eye, MG3!

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I had "level payment with balloon after X payments" on the brain, and pulled the trigger too quick.

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Yeah, I usually have that on the brain too. I don't know what made me pull out the calculator and see what those payments added up to. Luck?

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With OP's opening line about "total principal of 3M", and then the method OP used in the calcs, I'm inclined to think it's an "even principal plus interest" scenario, rather than "PV of 15 payments of 200K" kinduva thing.

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I would agree. I was just trying to think of an alternative possibility.

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Thanks for the sharp eye, MG3!

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That's funny -- I'm actually really, really tired right now. Maybe I should do this when I'm asleep more often. :p

Thank you so much to both of you.

I think I have to explain the situation more further. But I think this is not the proper place to discuss. I hope you understand. I have a Yahoo messenger account, is it possible chatting with you on this website? I am an accounting graduate but not a cpa. I really need help from an expert.

Waiting for your response. Thank you.

An expert at what in particular? There really isn't anyone here who is what I'd call a good "all-around" person who can work on any topic. We sort of all deal with the things we can do the best, in theory anyway. :D Is it this same type of stuff?

Do you feel this is going to get too private to post here?

We do not have an instant messaging system, no. We do have a private messaging system -- i.e. that works exactly like this (posting back and forth), but is not on the public forums. You have to have some minimum amounts of post to do that though, I don't know the number cause that's a change from when I started. (It's not 5 cause yours isn't showing yet. Maybe it's 10.) If you can get a few more posts in, you can try that.

I have AIM and ICQ but not Yahoo. However, I don't give those ID's out in public, so you'd still have to PM me. Can't speak for anyone else of course.

Yes, the situation is still the same and it's a private thing. I just want to make sure that the interest is properly computed before we make this thing as an "exhibit".

Just want to ask you again if the interest can be computed based on the monthly installment amount (200,000.00) against the number of days due. It is my understanding that the interest will vary depending on each due date and amount and not on the whole principal amount which is the 3,000,000.00. With those schedule of payment, no payment has been made yet.

My boss told me that interest should not earned interest.

I need to know the total interest, the daily interest and what is the present value of the 3,000,000.00.

Thank you.

OK, sounds like you're structuring a promissory note, say, as part of a buyout deal or a proposed biz financing arrangement. Without disclosing any sensitive info, can you describe in more detail the terms of this arrangement?

If the deal terms have already been agreed upon and locked into place, then I'm sure we could give you some guidance re your questions. If, on the other hand, you're at that stage of the deal where you're wanting to explore "options" regarding different possible note structures and valuations, then you'd be much better off with a local advisor who could, given access to the details, help you run different "what if" scenarios.

But as I mentioned, if you could describe the details a bit more, it's much more likely we'd have enough to go on, in order to give some advice. Thanks!

I agree with ArcSine, but I will add a couple of things.

For one, as to the interest being done by the day as you've done it, or as 1/12th of a year as ArcSine suggest, isn't a rule. If it's a situation where one party is "in charge" then they have their terms and that's how it works. (For instance, if I get a bank loan, I will have choices about certain things, but the precise way in which they calculate the interest is going to be using their standards.) If it's negotiable, that's different, and you can negotiate whatever you want.

Waiver: unless there's something going on here that we are not privy to that might "dictate" how it should be done, but I can't think what.

The interest earning interest... the only way that could happen is if a payment isn't made on time and interest is accrued as of that date, thereby increasing the amount due. Interest can be charged on that. (Like what a credit card would do.) But that again would be part of the agreement.

Now, as to charging interest only on the 200,000 payment, I would certainly not call that normal. If you did that, then the interest on the other 2,800,000 left after the first payment would keep accruing. That is, when the second payment was made, there would be interest of two months on that 200,000 payment. Then interest for three months on the next 200,000 payment, etc. That's also not the way you did it in your first post.

What you originally did was charging interest on the unpaid principle. So first payment would be the 200,000 plus the interest on the 3 million. Then next would be 200,000 plus interest on 2.8 million (after reducing principle).