Find the value of 

$ 10 comma 000$10,000 

at the end of one year if it is invested in an account that has an interest rate of 

4.05 %4.05% 

and is compounded in accordance with the rules below.

**a.** compounded monthly

**b.**

 compounded daily​ (assuming a​ 365-day year)

**c.**

 compounded quarterly

Question content area bottom

Part 1

**a.** What is the value if the money is compounded​ monthly?

​$10412.6010412.60

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Part 2

**b.**What 

is the value if the money is compounded​ daily?

​$10413.2910413.29

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Part 3

**c.** What is the value if the money is compounded​ quarterly?

​$enter your response here

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

answer part C

To find the value of an investment compounded quarterly, we use the formula for compound interest:

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

Where:
- $ A $ is the final amount
- $ P = 10,000 $ is the initial principal (investment)
- $ r = 0.0405 $ is the annual interest rate (4.05%)
- $ n = 4 $ is the number of times the interest is compounded per year (quarterly)
- $ t = 1 $ is the time in years

### Step 1: Plug the values into the formula

\[
A = 10,000 \left(1 + \frac{0.0405}{4}\right)^{4(1)}
\]
\[
A = 10,000 \left(1 + 0.010125\right)^4
\]
\[
A = 10,000 \left(1.010125\right)^4
\]

### Step 2: Calculate $ \left(1.010125\right)^4 $

\[
A = 10,000 \times 1.041051
\]

### Step 3: Calculate the final amount

\[
A = 10,410.51
\]

Thus, the value of the investment compounded quarterly is **$10,410.51**.

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Would you like further details, or do you have any questions?

Here are some related questions:

1. What would the value be if compounded weekly instead of quarterly?
2. How does the frequency of compounding affect the final amount?
3. What is the formula for continuous compounding?
4. What is the effective annual rate (EAR) for each of these compounding frequencies?
5. How would this change if the interest rate was 5% instead of 4.05%?

**Tip:** The more frequently interest is compounded, the higher the final amount will be!

Find the value of $10,000 at the end of one year if it is invested in an account that has an interest rate of 4.05% and is compounded in accordance with the rules below.

a. compounded monthly
b. compounded daily (assuming a 365-day year)
c. compounded quarterly

Discover how to calculate the value of $10,000 after one year with a 4.05% interest rate. Learn about monthly, daily, and quarterly compounding, including step-by-step solutions for each method. Ideal for students in Grades 10-12 learning financial mathematics.

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