
Question content area top

Part 1

Find the interest rate for 

aa 

​$95009500 

deposit accumulating to 

​$11 comma 87811,878​, 

compounded annually for 

88 

years.

Question content area bottom

Part 1

The interest rate is 

enter your response here​%.

​(Do not round until the final answer. Then round to two decimal places as​ needed.)

To find the interest rate, we use the compound interest formula:

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

Given:
- $ A = 11,878 $
- $ P = 9,500 $
- $ n = 1 $ (compounded annually)
- $ t = 8 $ years

We need to solve for $ r $:

\[
11,878 = 9,500 \times \left(1 + r\right)^{8}
\]

First, divide both sides by 9,500:

\[
\frac{11,878}{9,500} = \left(1 + r\right)^{8}
\]

\[
1.2503 = \left(1 + r\right)^{8}
\]

Next, take the 8th root of both sides:

\[
1 + r = 1.2503^{\frac{1}{8}}
\]

\[
1 + r \approx 1.0276
\]

Finally, subtract 1 from both sides to find $ r $:

\[
r \approx 1.0276 - 1
\]

\[
r \approx 0.0276
\]

Convert $ r $ to a percentage:

\[
r \approx 2.76\%
\]

So, the interest rate is **2.76%**.

Would you like more details or have any questions?

Here are some related questions:
1. How does the interest rate affect the accumulated amount over different time periods?
2. What would be the final amount if the interest rate was slightly higher, say 3%?
3. How can the compound interest formula be adjusted for quarterly compounding?
4. How does inflation affect the real interest rate?
5. How does a longer compounding period (e.g., 15 years) change the interest rate for the same final amount?

**Tip:** When using compound interest formulas, ensure that the time and interest rate are both correctly aligned with the compounding period.

Learn how to calculate the interest rate for a $9,500 deposit accumulating to $11,878 over 8 years, compounded annually. Follow a step-by-step solution using the compound interest formula.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation