Use the compound interest formula,  A(t)=P(1+rn)nt
 .

 

After a certain number of years, the value of an investment account is represented by the expression  10,350(1+0.0412)108
 . What is the value of the account?

Round your answer to two decimal places.

 The value of the account is  $
   



We are given the expression for the value of the investment account as:

\[
A(t) = 10,350(1 + 0.0412)^{108}
\]

Where:
- $ P = 10,350 $ is the principal (initial investment),
- $ r = 0.0412 $ is the annual interest rate,
- $ n = 108 $ is the number of compounding periods (this might imply monthly compounding for 9 years, as 108 months is 9 years).

We now calculate the value of the account by simplifying the expression.

\[
A(t) = 10,350 \times (1.0412)^{108}
\]

I'll compute this value.The value of the account is approximately \$810,269.64 after the specified period.

Would you like more details on how the calculation was done, or do you have any questions?

Here are 5 related questions for practice:
1. How would the account value change if the interest rate increased to 5%?
2. What if the investment period was extended to 120 months with the same interest rate?
3. How would the value change with semi-annual compounding instead of monthly?
4. If the initial investment was \$15,000, what would the account value be after the same period?
5. How long would it take for the investment to double with this interest rate?

**Tip:** Compound interest grows faster when compounded more frequently (e.g., monthly vs. annually).

After a certain number of years, the value of an investment account is represented by the expression 10,350(1+0.0412)^108. What is the value of the account? Round your answer to two decimal places.

Calculate the future value of an investment account using the compound interest formula. Given an initial investment of $10,350 and an interest rate of 4.12%, we compute the account value after 108 compounding periods. Learn how to solve this step-by-step, suitable for Grades 10-12.

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