Which one would earn more for a Savings account? Compounding Interest Daily vs. Monthly?
Lets take the example from the Discover website. the Discover Online Savings Account vs the Cap1 360 Savings Account
Both accounts are 1.90% APY with a savings amount of $15k. but on the Cap1 Interest is compounded monthly and earns $3.06 more, why is that?
i don't understand the math. how do you calculate all this stuff? and what's the different between APY and APR?
Thanks for all the support!
All other things equal, compounding daily is better than monthly. The figures shown on the Discover website don't show everything.
But, the difference between APR and APY is simple enough to explain in a quick post. APR is calculation of simple interest. It's the actual percentage rate of annual interest applied to the account when the interest compounds. If an account compounded annually, APR and APY would be the same. But, if interest compounds more often, APY will be higher. Why? Because after interest compounds, you start earning interest on the interest.
To make the math simple, let's assume an account with a 1.2% APR, starting with $10,000, that compounds monthly. Every month, you earn one month of that APR, so 1/12 of 1.2% or 0.1%.
Month 1: Balance of $10000.00 earns 0.1% or $10.00. So you wind up with $10010.00.
Month 2: Balance of $10010.00 earns 0.1% or $10.01. So you wind up with $10020.01.
Month 3: Balance of $10020.01 earns 0.1% or $10.02. So you wind up with $10030.03.
Month 4: Balance of $10030.03 earns 0.1% or $10.03. So you wind up with $10040.06.
Month 5: Balance of $10040.06 earns 0.1% or $10.04. So you wind up with $10050.10.
Month 6: Balance of $10050.10 earns 0.1% or $10.05. So you wind up with $10060.15.
Month 7: Balance of $10060.15 earns 0.1% or $10.06. So you wind up with $10070.21.
Month 8: Balance of $10070.21 earns 0.1% or $10.07. So you wind up with $10080.28.
Month 9: Balance of $10080.28 earns 0.1% or $10.08. So you wind up with $10090.36.
Month 10: Balance of $10090.36 earns 0.1% or $10.09. So you wind up with $10100.45.
Month 11: Balance of $10100.45 earns 0.1% or $10.10. So you wind up with $10110.55.
Month 12: Balance of $10110.55 earns 0.1% or $10.11. So you wind up with $10120.66.
With an APR of 1.2% and compounding monthly, your APY ends up being 120.66/10000 = 1.2066%. Slightly higher than the APR.
Compounding daily would give you a higher APY relative to APR>
But with these accounts, they're advertising the APY, not the APR, so you're seeing what you actually will earn, with compounding, if you park your money there for a year. Assuming the Cap1 figures are correct, their APR may be a little higher, and the APY rounds off to the same number.