calculate the compound amount and compound interest (in $) for the investment. (Round your answers to the nearest cent.)
Principal	Time 24000
Period (years) 16 yrs Nominal
Rate (%)	5 Interest
Compounded anually
Amount	Compound
Interest
$24,000	16	5	annually

To calculate the compound amount and compound interest for the given investment, we can use the compound interest formula:

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

Where:
- $A$ is the amount of money accumulated after $n$ years, including interest.
- $P$ is the principal amount (the initial money before interest).
- $r$ is the nominal annual interest rate (as a decimal).
- $n$ is the number of times that interest is compounded per year.
- $t$ is the time the money is invested or borrowed for, in years.

Given:
- $P = 24{,}000$ dollars
- $r = 5\%$ or $0.05$
- $n = 1$ (since the interest is compounded annually)
- $t = 16$ years

### Step 1: Calculate the Compound Amount (A)
\[
A = 24{,}000 \left(1 + \frac{0.05}{1}\right)^{1 \times 16}
\]
\[
A = 24{,}000 \left(1 + 0.05\right)^{16}
\]
\[
A = 24{,}000 \times (1.05)^{16}
\]
Let's calculate the value of $(1.05)^{16}$ and then multiply by the principal.

### Step 2: Calculate Compound Interest
Compound Interest = Amount $-$ Principal

Now, I'll calculate these values.### Results:
- **Compound Amount (A):** $52,388.99
- **Compound Interest:** $28,388.99

These amounts are rounded to the nearest cent as requested.

Would you like more details or have any questions?

### Related Questions:
1. How would the result change if the interest were compounded quarterly instead of annually?
2. What would be the compound interest if the investment period was 10 years instead of 16?
3. How would the compound amount change if the interest rate was 6% instead of 5%?
4. What happens to the compound interest if the principal was $30,000 instead of $24,000?
5. How does continuous compounding affect the final amount compared to annual compounding?

### Tip:
Always double-check the compounding period (annually, quarterly, monthly, etc.) as it significantly affects the final amount.

Learn how to calculate compound amount and compound interest for an investment of $24,000 at an annual interest rate of 5%. Detailed step-by-step solution included, rounded to the nearest cent.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation