Student Loan Inquiry

[jmadero]

Hi All,

First post, thanks for the help in advance, I'm a forum junky

Moving on, I'm in the process of writing software code for a debt management program. I'm using my wife's student loan as test cases and can't for the life of me figure out how they are getting their numbers. I have a background in Economics but very little accounting experience. Here's the numbers:

Loan -- Compounded Daily
Principle -- $5,740
Interest -- 8.5%
Disbursement Day: 9/26/2008


All I want to know is what would the current amount be given no payments made. My numbers (as well as others who have tested this for me) have all been different from theres, pretty frustrating, and of course, they are no help answering questions

 

[ArcSine]

Under daily compounding, if some principal amount P has been outstanding for n days, and the annual interest rate is r (expressed as a decimal, such as r = 0.085), then the total principal and interest due after n days is given by

P(1 + r / 365)^n

Of course, you could deduct P from the result to determine the interest that's accrued over the n days.

Sometimes in daily compounding situations, one might use a continuous-compounding formula instead, since it'll approximate the more exact daily compounding result closely enough for most purposes, and is usually a simpler expression to deal with. This might account for some of the differences you're getting from other sources.

 

[jmadero]

My difference is relatively large using exactly that formula that you gave me. I emailed them to try to get an explanation out of them. I need it to be exact for the software that I am writing so I really need to understand the fundamentals of how they are getting their numbers.

 

[bklynboy]

Hi All,

First post, thanks for the help in advance, I'm a forum junky

Moving on, I'm in the process of writing software code for a debt management program. I'm using my wife's student loan as test cases and can't for the life of me figure out how they are getting their numbers. I have a background in Economics but very little accounting experience. Here's the numbers:

Loan -- Compounded Daily
Principle -- $5,740
Interest -- 8.5%
Disbursement Day: 9/26/2008


All I want to know is what would the current amount be given no payments made. My numbers (as well as others who have tested this for me) have all been different from theres, pretty frustrating, and of course, they are no help answering questions

What is the end date that the calculation is being based on (i.e. is it 12/31/2011 or a different date)? What is the amount they are quoting on the statement that we need to determine? If you provide these pieces I think we can help with the result.

If I assume a date of 12/31/2011 as the statement date, I come up with 7,574 as the loan and interest balance due.

 

[ArcSine]

Also, JMadero, check the terms of the loan agreement very carefully. Loan contracts have ways of defining terms and/or inserting special provisions which can make the actual calculation different that what you might expect. Many loan agreements, for example, utilize a 360-day day-count convention, wherein it's assumed (for purposes of interest accrual) that a year consists of 360 days.

Hence, the wrinkles that a contract builds in often mean that a formula can't be used in its straight-out-the-textbook form, but instead have to be tweaked to allow for the contract's specific terms and definitions.

Also, since the diffs you're seeing are significant, they're not coming from the possible use of a continuous-compounding assumption I alluded to earlier. As Bklynboy noted, the accumulated amount at Dec 31 2011 is 7,574.47 under a daily compounding approach, whereas continuous compounding puts it at 7,574.71 --- hardly the "relatively large" differences you've noted.