Ferb puts $800 into a certificate of deposit that earns 3.88%. If the money is compounded quarterly, how much will it be worth in 4 years?

 

State your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.

 

To solve this problem, we will use the compound interest formula:

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

Where:
- $ A $ is the final amount (what we're solving for).
- $ P = 800 $ is the principal amount (initial investment).
- $ r = 0.0388 $ is the annual interest rate (3.88%).
- $ n = 4 $ is the number of times the interest is compounded per year (quarterly).
- $ t = 4 $ is the number of years.

Now, let's calculate:

\[
A = 800 \left(1 + \frac{0.0388}{4}\right)^{4 \times 4}
\]

I'll compute that now.The final amount after 4 years will be approximately **933.61**.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:
1. What is the formula for continuous compounding interest?
2. How would the total amount change if the interest was compounded monthly instead of quarterly?
3. What would happen if Ferb withdrew his money before the 4 years were up?
4. How would the total change if the interest rate increased to 5%?
5. Can you calculate the total interest earned over the 4 years?

**Tip:** Always double-check the compounding frequency when solving interest problems, as it can significantly affect the final amount.

Ferb puts $800 into a certificate of deposit that earns 3.88%. If the money is compounded quarterly, how much will it be worth in 4 years?

Learn how to calculate the compound interest for a $800 investment at a 3.88% interest rate, compounded quarterly for 4 years. This problem illustrates key concepts such as compound interest and exponential growth, providing a step-by-step solution using the formula A = P(1 + r/n)^(nt). Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation