How much money will there be in an account at the end of 7 years if $2000 is deposited at 4% interest compounded semi-annually? (Assume no withdrawals are made.) The amount after 7 years will be (Round to the nearest cent as needed.)
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Algebraic Modeling
![**Compound Interest Calculation**
**Problem Statement:**
How much money will there be in an account at the end of 7 years if $2000 is deposited at 4% interest compounded semi-annually? (Assume no withdrawals are made.)
**Solution:**
To calculate the future value of an investment with compound interest, use the 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 (initial investment).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times interest is compounded per year.
- \( t \) is the time the money is invested for in years.
Given:
- \( P = 2000 \)
- \( r = 0.04 \)
- \( n = 2 \) (since the interest is compounded semi-annually)
- \( t = 7 \)
Substituting the given values into the formula:
\[ A = 2000 \left(1 + \frac{0.04}{2}\right)^{2 \times 7} \]
\[ A = 2000 \left(1 + 0.02\right)^{14} \]
\[ A = 2000 \times (1.02)^{14} \]
Calculate the final amount:
The amount after 7 years will be \$____. (Round to the nearest cent as needed.)
**Instructions:**
Complete the calculation and fill in the blank with the rounded amount.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba8e985f-7622-401b-bed1-843294526707%2Fd6ec10c3-e639-4ea4-b158-4f79fe750452%2Fw078lvb_processed.png&w=3840&q=75)
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