I am enrolled in the live online class. We are currently working through book 10.

I do not understand the answer given for drill question 10. Please let me know if I am missing something. Or perhaps is the book wrong?

Drill question 10 on page 59 of book 10 reads: Convert a semi-annual compounded interest rate of 10% to an annual compounded interest rate.

My understanding of compounded interest rates is that in order to calculate the total interest rate for the year, you have to divide the interest rate by the number of times it is compounded - 2 in this case since it is semi-annual - and then multiply that through for for the number of periods.

So you would multiply by a 5% interest rate twice: 1.05 * 1.05 which results in 1.1025 or a 10.25% interest rate if it were compounded annually rather than semi-annually.

That is how I would solve it, yet the back of the book states that the answer is 21%. Curious.

Please tell me where I am making an error. Am I misunderstanding what the question is asking?

Actually, a semi-annual interest rate of 10% means that 10% is charged every 6 months.
If we simply added 10% to 10% for each 6 month period, we'd get 20% annual, but this would be simple, not compound.

Look at it this way --
If we start with $100, and we get charged 10% after 6months, we owe $110.
6 months later (at the end of 1 year) we owe 1.1*$110, which is $121.

This is effectively 21% interest on an annual basis.

Veritas Help

I see. I guess I was reading it to be 10% annual interest compounded semi annually