# 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.

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

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.

I found an answer from www.purplemath.com

**Exponential Functions**: **Compound Interest**

You want to invest in an instrument yielding 3.5% interest, **compounded monthly**.
How much should you invest? To solve this, I have to **figure out** which values go ...

For more information, see **Exponential Functions**: **Compound Interest**