wiki wrote:There are two ways of expressing compound interest. Although the results are identical, the manner in which the interest rates are presented has implications to borrowers and lenders. As defined below, Annual Percentage Rate (APR) is always a lower number than Annual Percentage Yield (APY).
* Lenders, such as banks or other institutions, will quote the higher APY to entice customers. For example, bank savings accounts are advertised using APY, as customers are looking for the highest rates.
* Borrowers looking for the lowest rates will be attracted to the lower APR. For example, mortgages and automobile loans use APR to entice borrowers with low rates.
Compounding Effective Rate (APY) Future Value
quarterly (4) 10.38% =EFFECT(10%,4) $1,103.81 =FV(10.38%,1,0,-1000)
monthly (12) 10.47% =EFFECT(10%,12) $1,104.71 = FV(10.47%,1,0,-1000)
daily (365) 10.52% =EFFECT(10%,365) $1,105.16 = FV(10.52%,1,0,-1000)
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:zrzhu111 wrote:How do you convert the rate for daily/quarterly/monthly compounding to APY?
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).zrzhu111 wrote:I think I figured it out. ... APR= 0.009 compounding daily =10000*(1+0.009/365)^365= 10090.405098137
#Cruncher wrote: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
zrzhu111 wrote:Thanks. I think I figured it out.
APR=0.01 compounding monthly
=10000*(1+0.01/12)^12=10100.4596088718
APR= 0.009 compounding daily
=10000*(1+0.009/365)^365= 10090.405098137
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