Household Math: Compounded Daily vs. Monthly

You have $10,000 that you want to deposit in a money market account. You have a choice between two accounts. Both accounts pay 5% APR (Annual Percentage Rate). One account is compounded daily, meaning that interest is paid daily to the account. The other is compounded monthly meaning that interest is paid monthly. After one year, how much more is earned by depositing the money in the account that is compounded daily? ($1.05, $10.05, $100.05, or $1,000.05)

ANSWER
$1.05

EXPLANATION
Many people assume that the faster compounding will make a huge difference in the final amount earned, or in the case of loans, the amount paid. The truth is that there is an affect, but it’s not as big as you may think.

First you need to compute the Periodic Rate. This rate is based on the APR. If the period is months, then the periodic rate is the APR divided by 12.

Monthly Rate = 5% / 12 = 0.41666% (Periodic Rate)

The Effective Rate is the total percentage gained from one point in time to another, usually one year. Another name for that is the APY (Annual Percentage Yield).

In this case it’s (1 + monthly rate)^12. That means, (1 + monthly rate) x (1 + monthly rate) x (1 + monthly rate)…twelve times (because there are 12 monthly periods in one year).

APY + 1 = (1.0041666)^12 = 1.051162

APY = 5.1162%

Total interest paid on monthly account = $511.62.

The period of the daily account is days. The daily rate is 5% divided by 365.

Daily Rate = 5% / 365 = 0.013698

APY + 1 = (1.00013698)^365 = 1.051267

APY = 5.1267%

Total interest paid on daily account = $512.67

Difference is $1.05 ($512.67 – $511.62).