How does interest payments on LOC work?

[Dionysus]

I'm a little confused on how much interest is paid on the amount of LOC that I take out. Say I take out $100k worth of loans and the interest is at 3% (assuming I take out 100k on day 1), I should be paying 3% per year right? So I should be paying 3k a year on interest charges and for four years I would be paying 12k total interest. Any explanation would be much appreciated. I'm with RBC if that helps at all.

[Lonney]

You are forgetting about compound interest which is quite deadly

 

After four years, you end up paying 12551$ in interest

[Merquise]

To elaborate on what Lonney said above, it's a matter of how often the bank charges you for interest. If the bank charged you the 3% annual interest as a lump sum after 4 years, you would be correct that it would be 12k in interest. But instead, you get charged monthly by the bank.

 

Then comes the matter of how you'll pay for the interest. With you being 100k in debt, chances are that you'll be paying it with the LoC. This means that the monthly interest payment will grow the LoC every month and cause next month's interest payment to be larger (compound interest).

 

A more realistic interest rate to go by with compounding is the Effective Annual Rate (EAR). To get this number, we take the 3% Annual Percentage Rate (APR) in decimal form and use the following formula:

 

EAR = (1 + APR/i)^i - 1

where "i" is the number of times you'll be charged per year (i = 12 in this case)

 

Thus, EAR = (1 + 0.03/12)^12 - 1 = 0.0304 or 3.04%, which is actually how much your debt will be growing per year.

 

So in 4 years, your debt will go from $100,000 to 100,000 * 1.0304 * 1.0304 * 1.0304 * 1.0304 = $112,733. Your interest on the loan is effectively $12,733.

 

EDIT: (If it's the case mentioned by ralk below that the 3% is an EAR, then your debt grows to 100,000 * 1.03 * 1.03 * 1.03 * 1.03 = $112551, so the interest would be $12,551 as mentioned by Lonney)

 

Sorry for the wall of text... it's the math tutor in me lol

[ralk]

To elaborate on what Lonney said above, it's a matter of how often the bank charges you for interest. If the bank charged you the 3% annual interest as a lump sum after 4 years, you would be correct that it would be 12k in interest. But instead, you get charged monthly by the bank.

 

Then comes the matter of how you'll pay for the interest. With you being 100k in debt, chances are that you'll be paying it with the LoC. This means that the monthly interest payment will grow the LoC every month and cause next month's interest payment to be larger (compound interest).

 

A more realistic interest rate to go by with compounding is the Effective Annual Rate (EAR). To get this number, we take the 3% Annual Percentage Rate (APR) in decimal form and use the following formula:

 

EAR = 1 - (1 + APR/i)^i

where "i" is the number of times you'll be charged per year (i = 12 in this case)

 

Thus, EAR = 1 - (1 + 0.03/12)^12 = 0.0304 or 3.04%, which is actually how much your debt will be growing per year.

 

So in 4 years, your debt will go from $100,000 to 100,000 * 1.0304 * 1.0304 * 1.0304 * 1.0304 = $112,733. Your interest on the loan is effectively $12,733.

 

Sorry for the wall of text... it's the math tutor in me lol

 

Most rates in Canada are stated as effective annual rates. That is, the 3% charged will not be affected by frequency of compounding - that's already accounted for.

[Merquise]

Most rates in Canada are stated as effective annual rates. That is, the 3% charged will not be affected by frequency of compounding - that's already accounted for.

 

From what I read on the contract when I signed with RBC, I'm 90% sure 3% is APR at least for RBC

 

Will find loan agreement and try to double-check tomorrow morning

[bordeaux]

Most rates in Canada are stated as effective annual rates. That is, the 3% charged will not be affected by frequency of compounding - that's already accounted for.

 

Sorry, that's not true unless you actually pay the interest off every month using something other than a debt facility to do so. So to be very simplistic (actual calculation is based on your daily balance and added at the end of the cycle) if you have a balance of $50,000 for a full year at 3%, monthly interest is of course, 50000 x .03 / 12 = $125. If however, your interest payment is just added to the credit line (which is the reality for most of us) you're then accruing interest on the interest as well. Stated interest is still 3% but the EAR is as shown in the post by Merquise. After a year of using mine and watching that balance skip its merry way upwards, it's all become very clear.

[gerywilliam]

nice post.

[b3ck1]

To elaborate on what Lonney said above, it's a matter of how often the bank charges you for interest. If the bank charged you the 3% annual interest as a lump sum after 4 years, you would be correct that it would be 12k in interest. But instead, you get charged monthly by the bank.

 

Then comes the matter of how you'll pay for the interest. With you being 100k in debt, chances are that you'll be paying it with the LoC. This means that the monthly interest payment will grow the LoC every month and cause next month's interest payment to be larger (compound interest).

 

A more realistic interest rate to go by with compounding is the Effective Annual Rate (EAR). To get this number, we take the 3% Annual Percentage Rate (APR) in decimal form and use the following formula:

 

EAR = (1 + APR/i)^i - 1

where "i" is the number of times you'll be charged per year (i = 12 in this case)

 

Thus, EAR = (1 + 0.03/12)^12 - 1 = 0.0304 or 3.04%, which is actually how much your debt will be growing per year.

 

So in 4 years, your debt will go from $100,000 to 100,000 * 1.0304 * 1.0304 * 1.0304 * 1.0304 = $112,733. Your interest on the loan is effectively $12,733.

 

EDIT: (If it's the case mentioned by ralk below that the 3% is an EAR, then your debt grows to 100,000 * 1.03 * 1.03 * 1.03 * 1.03 = $112551, so the interest would be $12,551 as mentioned by Lonney)

 

Sorry for the wall of text... it's the math tutor in me lol

 

 

I think it's great that you actually explained that well!!! now i understand it and i can apply it for other rates and other amounts of loans! So don't apologize for the math tutor in you! As far as i am concerned, your math tutor is highly appreciate it!

[ralk]

From what I read on the contract when I signed with RBC, I'm 90% sure 3% is APR at least for RBC

 

Will find loan agreement and try to double-check tomorrow morning

 

Hmm, checked my own and yes, you seem to be correct.