
Question content area top

Part 1

Use the compound interest formula to determine the accumulated balance after the stated period.

​$40004000 

invested at an APR of 

77​% 

for 

66 

years.

Question content area bottom

Part 1

If interest is compounded​ annually, what is the amount of money after 

66 

​years?

​$enter your response here

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


The compound interest formula is:

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

where:
- $ A $ = the accumulated balance (future value),
- $ P $ = the principal (initial amount) = $4000,
- $ r $ = annual interest rate (APR) = 7% or 0.07,
- $ n $ = number of times interest is compounded per year = 1 (annually),
- $ t $ = the number of years = 6.

Let's substitute these values into the formula.

### Step-by-Step Solution:
1. Substitute the values into the formula:
   \[
   A = 4000 \left(1 + \frac{0.07}{1}\right)^{1 \cdot 6}
   \]

2. Simplify inside the parentheses:
   \[
   A = 4000 \left(1 + 0.07\right)^6 = 4000 \left(1.07\right)^6
   \]

3. Calculate $ (1.07)^6 $.

4. Multiply by 4000.

Let me calculate this for you.The accumulated balance after 6 years, with an APR of 7% compounded annually, is approximately $6002.92.

Would you like more details on any of the steps? 

Here are some related questions for practice:
1. How would the balance change if the interest were compounded quarterly?
2. What is the balance if the APR were 5% instead of 7%?
3. How much interest is earned in total over the 6 years?
4. How would you find the future balance if interest were compounded continuously?
5. What would be the balance after 10 years with the same APR and compounding annually?

**Tip:** When calculating compound interest, double-check if the compounding frequency (annually, semiannually, quarterly, etc.) affects your results.

Use the compound interest formula to determine the accumulated balance after the stated period. $4000 invested at an APR of 7% for 6 years. If interest is compounded annually, what is the amount of money after 6 years? (Do not round until the final answer. Then round to the nearest cent as needed.)

Learn how to calculate compound interest on $4000 at a 7% APR compounded annually over 6 years using the formula A = P(1 + r/n)^(nt). Includes a step-by-step solution and rounded final answer. Suitable for Grades 9-12 students.

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