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Hi,
I can’t get my head around the APR question from the December 2005 exam. I’ll type out the relevant part.
The after-tax borrowing rate of 7% was used in the evaluation because a bank had offered to lend AGD Co $320,000 for a period of five years at a before-tax rate of 10% per year with interest payable every six months.
Required: Calculate the APR implied by the bank’s offer to lend at 10% per year with interest payable every six months.
Answer: As interest is due every six months, this is equivalent to 5% every six months. As this would be compounded, therefore the APR would be (1.05 x 1.05 – 1) = 0.1025 or 10.25%.
I’m not sure why paying every six months implies a higher interest rate. My BPP book doesn’t seem to have anything on APR. Do you have any lectures here on it?
Thanks for your help.
It is because they charge 5% after six month, which means for every 100 borrowed you now owe 105. Then they charge another 5% six months later on the whole 105, which means that after the year you owe a total of 110.25.
So this is equivalent to having been charged 10.25 interest over a year, or 10.25%There is a lecture that includes this in the F2 lectures (it is the chapter on interest).
Thanks very much for your explanation. I’ll watch the F2 lecture. I’m a bit ashamed I’ve forgotten a lot of the stuff from my earlier studies!
I think my confusion might be because I assumed that if they charge interest every six months, the interest would be paid straight away, but that’s not the case, is it? The interest just increases the size of the loan?
Sorry, I’m still not 100% clear! In the question, it states that interest is payable every six months. Therefore, if they pay the interest off every six months, why does the size of the loan increase? I thought it would stay the same.
I know that the English is confusing, but in this sort of question payable does not really mean paid. If they did actually pay it (and not leave it owing) then they would only actually pay $10. However the fact that they were paying half of it in 6 months does mean it is ‘worse’ for them than just paying $10 at the end of the year as would normally happen. If they have to pay half it earlier then it means they would either have to borrow it or use money that they could otherwise have been earning interest on.
Thanks for clarifying that for me. For exam purposes then I’ll assume that payable is synonymous with chargeable!
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