Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To find the future value of Mary's investment using the compound interest formula, we follow these steps:
1. Identify the given values:
- Principal amount ([tex]\( P \)[/tex]) = \[tex]$1000 - Annual interest rate (\( r \)) = 0.05 (since 5% as a decimal is 0.05) - Number of times interest is compounded per year (\( n \)) = 4 - Number of years (\( t \)) = 5 2. Write the compound interest formula: \[ R = P \left(1 + \frac{r}{n}\right)^{nt} \] 3. Substitute the given values into the formula: \[ R = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \cdot 5} \] 4. Calculate the value inside the parentheses: \[ 1 + \frac{0.05}{4} = 1 + 0.0125 = 1.0125 \] 5. Calculate the exponent: \[ nt = 4 \cdot 5 = 20 \] 6. Raise the value inside the parentheses to the power of 20: \[ (1.0125)^{20} \] 7. Multiply this result by the principal amount (\( P \)): \[ R = 1000 \times (1.0125)^{20} \approx 1000 \times 1.2820372317085844 \] 8. Calculate the final amount: \[ R \approx 1282.0372317085844 \] So, the future value of Mary's investment after 5 years will be approximately \$[/tex]1,282.04.
Based on the calculations, the correct answer is:
[tex]\[ \$ 1,282.04 \][/tex]
1. Identify the given values:
- Principal amount ([tex]\( P \)[/tex]) = \[tex]$1000 - Annual interest rate (\( r \)) = 0.05 (since 5% as a decimal is 0.05) - Number of times interest is compounded per year (\( n \)) = 4 - Number of years (\( t \)) = 5 2. Write the compound interest formula: \[ R = P \left(1 + \frac{r}{n}\right)^{nt} \] 3. Substitute the given values into the formula: \[ R = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \cdot 5} \] 4. Calculate the value inside the parentheses: \[ 1 + \frac{0.05}{4} = 1 + 0.0125 = 1.0125 \] 5. Calculate the exponent: \[ nt = 4 \cdot 5 = 20 \] 6. Raise the value inside the parentheses to the power of 20: \[ (1.0125)^{20} \] 7. Multiply this result by the principal amount (\( P \)): \[ R = 1000 \times (1.0125)^{20} \approx 1000 \times 1.2820372317085844 \] 8. Calculate the final amount: \[ R \approx 1282.0372317085844 \] So, the future value of Mary's investment after 5 years will be approximately \$[/tex]1,282.04.
Based on the calculations, the correct answer is:
[tex]\[ \$ 1,282.04 \][/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.