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You may notice if you’re shopping for a savings account that banks advertise both an interest rate and an annual percentage rate, or APY.
So if you wanted to put $3,000—with no additional deposits—into a high-yield savings account earning 2% that compounds monthly (12 periods within a year), the APY formula would look like this ...
Annual percentage yield (APY) is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain.
Converting an annual interest rate (that is to say, annual percentage yield or APY) to the monthly rate is not as simple as dividing by 12; see the formula and discussion in APR. However, if the rate is stated in terms of "APR" and not "annual interest rate", then dividing by 12 is an appropriate means of determining the monthly interest rate.
For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% compounded monthly is credited as 6%/12 = 0.005 every month. After one year, the initial capital is increased by the factor (1 + 0.005) 12 ≈ 1.0617. Note that the yield increases with the frequency of compounding.
Let’s say you’re depositing $10,000 into a high-yield account with a 5% APY compounded monthly. You must convert the APY into a decimal by dividing the amount by 100. In this case, 5/100 = 0.05.
A formula that is accurate to within a few percent can be found by noting that for typical U.S. note rates (< % and terms =10–30 years), the monthly note rate is small compared to 1. r << 1 {\displaystyle r<<1} so that the ln ( 1 + r ) ≈ r {\displaystyle \ln(1+r)\approx r} which yields the simplification:
Key financial terms like APY and APR can be confusing to interpret, especially when factored into the true cost of borrowing money or the parameters of spending it. Whether you are looking for a...