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Part 1
The following money market account rates were available from a particular bank. Find the compound amount and the interest earned.
​$5000 at 1.06​% compounded daily for one year
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Part 1
The compound amount is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To find the compound amount for a money market account and the interest earned, we will use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- $ A $ is the compound amount (the total amount after interest),
- $ P $ is the principal (initial deposit),
- $ r $ is the annual nominal interest rate (expressed as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the time the money is invested for, in years.

### Given:
- $ P = 5000 $ (initial deposit),
- $ r = 0.0106 $ (1.06% annual interest rate),
- $ n = 365 $ (compounded daily),
- $ t = 1 $ year.

Let's substitute these values into the formula:

\[
A = 5000 \left(1 + \frac{0.0106}{365}\right)^{365 \times 1}
\]

### Step-by-step Calculation:

1. **Calculate the daily interest rate**:
   \[
   \frac{r}{n} = \frac{0.0106}{365} \approx 0.000029041
   \]

2. **Calculate the total number of compounding periods**:
   \[
   nt = 365 \times 1 = 365
   \]

3. **Plug these values into the formula and solve for $ A $**:
   \[
   A = 5000 \left(1 + 0.000029041\right)^{365}
   \]

Now let's compute this value:

\[
A = 5000 \times (1.000029041)^{365}
\]

We can calculate this step-by-step:

\[
A = 5000 \times 1.010633 \approx 5053.17
\]

### Compound Amount:
The compound amount after 1 year is **$5053.17**.

### Amount of Interest Earned:
The amount of interest earned can be found by subtracting the initial deposit from the compound amount:

\[
\text{Interest Earned} = A - P = 5053.17 - 5000 = 53.17
\]

### Summary:
- The compound amount after 1 year is **$5053.17**.
- The amount of interest earned is **$53.17**.

Would you like more details or have any questions?

### Related Questions:
1. How would the compound amount change if the interest rate was compounded monthly instead of daily?
2. What would be the compound amount for a deposit of $5000 at a 2% annual interest rate compounded daily for one year?
3. How much interest would be earned if the deposit was for two years instead of one year, keeping all other variables the same?
4. What is the effect of increasing the compounding frequency on the compound amount?
5. How would the total amount change if the initial deposit was $10,000 instead of $5000, with the same interest rate and compounding period?

### Tip:
For daily compounding, ensure you convert the annual interest rate to a daily rate by dividing by 365. This provides a more precise calculation for daily compounded interest.

Learn how to calculate the compound amount and interest earned for a money market account with daily compounding interest. Use the compound interest formula to find the total amount after one year with specific values like $5000 initial deposit and 1.06% annual interest rate.

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