A savings account pays a 3% nominal annual interest rate and has a balance of $1,000. Any interest earned is

deposited into the account and no further deposits or

withdrawals are made.

Write an expression that represents the balance in one

year if interest is compounded annually.

The compound interest formula by A = P\Big(1-\frac{r}{n}\Big)^\frac{n}{t}

where P is the initial amount which is $1000, the rate of interest is 0.03, n = 1 (since the interest is compounded once a year, annually), t = 1 year,

Plug in these find A = 1000(1-0.03)= 970

So, the balance in one year, of compounded annually is $970.

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I found an answer from money.stackexchange.com

Daily interest calculation combined with monthly compounding: Why ...

First, calculating interest on your bank account daily makes the most sense ... throughout the month: that is, you make deposits, and you make withdrawals. ... arriving at an amount of interest on some form of average balance, which is more fair to ... to know what the effective annual interest rate is with monthly compounding, ...

For more information, see Daily interest calculation combined with monthly compounding: Why ...

I found an answer from en.wikipedia.org

Rate of return - Wikipedia

For example, if an investor puts $1,000 in a 1-year certificate of deposit (CD) that pays an annual interest rate of 4%, paid quarterly, the CD would earn 1% interest  ...

For more information, see Rate of return - Wikipedia

This is the case of compound interest since the interest is deposited back into the and no further deposits or withdrawals are made.

P(1) = Principal after 1 year = P(0) + interest after one year = P(0) + r P(0) = (1 + r) P(0)

P(2) = Principal after 2 years = P(1) + interest after second year = P(1) + r P(1) = (1 + r) P(1) = (1 + r)^2 P(0).

So, the amount after t years = 1000 (1 + 0.03)^t = 1000 x 1.03^t.

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