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Finding the fintal amount in a word problem on compound interest
Suppose that is invested at a rate of , compounded semiannually. Assuming that no withdrawals are made, find the total amount after 3 ye
Do not round any intermediate computations, and round your answer to the nearest cent.

Ask by Ford Schofield. in the United States

Mar 27,2025

Question

O Expononh mad siponment punctions
Finding the fintal amount in a word problem on compound interest
Suppose that is invested at a rate of , compounded semiannually. Assuming that no withdrawals are made, find the total amount after 3 ye
Do not round any intermediate computations, and round your answer to the nearest cent.

Ask by Ford Schofield. in the United States

Mar 27,2025

UpStudy AI · Accepted Answer

**Step 1. Write the formula for compound interest.**  
The compound interest formula is:  
$$
A = P\left(1 + \frac{r}{n}\right)^{nt}
$$

**Step 2. Identify the values from the problem.**  
- Principal, $$ P = \$2000 $$  
- Annual interest rate, $$ r = 3.8\% = 0.038 $$  
- Number of times interest is compounded per year, $$ n = 2 $$ (semiannually)  
- Time in years, $$ t = 3 $$

**Step 3. Substitute the values into the formula.**  
$$
A = 2000\left(1 + \frac{0.038}{2}\right)^{2\times3} = 2000\left(1 + 0.019\right)^6
$$
$$
A = 2000\left(1.019\right)^6
$$

**Step 4. Compute $$\left(1.019\right)^6$$.**  
Using a calculator:  
$$
\left(1.019\right)^6 \approx 1.119708
$$

**Step 5. Multiply by the principal to find the final amount.**  
$$
A \approx 2000 \times 1.119708 \approx 2239.416
$$

**Step 6. Round the answer to the nearest cent.**  
$$
A \approx \$2239.42
$$
The total amount after 3 years is \$2,239.42.

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