zrzhu111 wrote:How do you convert the rate for daily/quarterly/monthly compounding to APY?
Read the section in the Wiki, Periodic interest rate
, just under the section Lady Geek
referenced. It explains the relationship between the "periodic rate", the APR, and the APY. Using the Wiki's formula, to convert from a daily periodic rate to APY would be:
APY = (1 + daily rate) ^ 365 - 1
The Wiki and several other web pages I examined show how to determine the APY given a daily periodic rate. But I didn't find any that show the reverse: how to calculate the daily periodic rate given the APY. To do this we need to alter the above formula to be:
daily rate = (1 + APY) ^ (1 / 365) - 1
Banks usually quote the APY -- not the APR -- for savings accounts, so that's probably what the 0.9% for the Barclays account is. Using the formula the daily rate is then:daily rate
= 1.009 ^ (1 / 365) - 1 = 0.002455%
To check this, we'll convert it back to the APY:APY
= 1.00002455 ^ 365 - 1 = 0.9%
If compounding is done monthly or quarterly instead of daily, use 12 or 4 instead of 365 in the above formulas. Now, you asked for an example ... Assume you deposit $1,000,000 in the Barclays account. The first day you would earn $24.55 in interest (1,000,000 X 0.002455%). After 30 days you'd earn $736.76 (1,000,000 X [1.00002455 ^ 30 - 1]). This is a whopping $0.26 more than the $736.50 you'd earn if interest weren't compounded daily (1,000,000 X 0.002455% X 30). After 365 days you'd earn $9,000 (1,000,000 X [1.00002455 ^ 365 - 1]).
Note: the "^" symbol denotes raising to a power. Most scientific calculators have a [y^x] key that does this.
zrzhu111 wrote:I think I figured it out. ... APR= 0.009 compounding daily =10000*(1+0.009/365)^365= 10090.405098137
That would be correct if the 0.9% were an APR. But I'm pretty sure Barclays is quoting an APY; in which case you'd end up with just $10,090.00. The corresponding APR is 0.896% using the formula in the Wiki (0.002455% X 365).