how does daily compounded interest work

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I have a high yield savings account that has an interest rate of 4% APY with an initial deposit of $6,000. The account compounds daily on the full account balance and is paid monthly.

Why is the account balance after 1 ~~day~~ month not $6,240 (4% of $6k), but instead $6,020.03? Why does it only reach approximately 4% in interest after a year has elapsed?

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3 Answers

Anonymous 0 Comments

It’s 4% **annual** interest compounded daily.

There are ~~365(.26)~~ 365(.24) days in a year, so it grows by 4/365 = 0.0109% per day. Although the value you listed is too high: it should have grown by only about 65 cents in the first day.

Anonymous 0 Comments

It’s 4% **annual** interest compounded daily.

There are ~~365(.26)~~ 365(.24) days in a year, so it grows by 4/365 = 0.0109% per day. Although the value you listed is too high: it should have grown by only about 65 cents in the first day.

Anonymous 0 Comments

It’s 4% **annual** interest compounded daily.

There are ~~365(.26)~~ 365(.24) days in a year, so it grows by 4/365 = 0.0109% per day. Although the value you listed is too high: it should have grown by only about 65 cents in the first day.