simple compounding problem

[angus]

When it says a deposit is compounded semiannually at 4%. and it wants you to calculate the accumulated value at the 4.25 years. Do you compound it 8 times with 0.02%? or do you just convert the interest rate into a quarterly compounded and calculate it based on that, which you would end up compounding it 17 times.

I'm just confused, in reality, would it be that when it says compounded semianually, it means it only compounds once half a year? or you can convert it to whatever compounding period you wish?

Thanks!

Angus

[BeanCounter]

No. 4% semiannually means 0.02 for half a year. Then sqrt(1.02) -1 is the effective interest rate for 0.25 year.

Therefore, [1.02^(4*2)] sqrt(1.02) will be the accumulated value of 1 dollar for 4.25 years.