Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To calculate the future value of an investment with the given parameters, we need to use the formula for compound interest. The formula to calculate the future value [tex]\( A \)[/tex] is given by:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{n \cdot t} \][/tex]
Here's a detailed step-by-step solution using the given values:
1. Identify the given values:
- Principal amount ([tex]\( P \)[/tex]) = \[tex]$21,000 - Annual interest rate (\( r \)) = 7\% or 0.07 (as a decimal) - Number of times the interest is compounded per year (\( n \)) = 12 (monthly) - Number of years (\( t \)) = 5 2. Plug the values into the formula: \[ A = 21,000 \left(1 + \frac{0.07}{12}\right)^{12 \cdot 5} \] 3. Calculate the periodic interest rate (\( \frac{r}{n} \)): \[ \frac{0.07}{12} \approx 0.0058333333 \] 4. Add the periodic interest rate to 1: \[ 1 + 0.0058333333 \approx 1.0058333333 \] 5. Calculate the exponent (\( n \cdot t \)): \[ 12 \cdot 5 = 60 \] 6. Raise the base to the power of the exponent: \[ (1.0058333333)^{60} \approx 1.41758 \] 7. Multiply the principal amount by the result from the previous step: \[ 21,000 \cdot 1.41758 \approx 29770.1358 \] 8. Round the final answer to two decimal places: \[ 29770.1358 \approx 29770.13 \] Therefore, the future value of the investment is \$[/tex]29,770.13.
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{n \cdot t} \][/tex]
Here's a detailed step-by-step solution using the given values:
1. Identify the given values:
- Principal amount ([tex]\( P \)[/tex]) = \[tex]$21,000 - Annual interest rate (\( r \)) = 7\% or 0.07 (as a decimal) - Number of times the interest is compounded per year (\( n \)) = 12 (monthly) - Number of years (\( t \)) = 5 2. Plug the values into the formula: \[ A = 21,000 \left(1 + \frac{0.07}{12}\right)^{12 \cdot 5} \] 3. Calculate the periodic interest rate (\( \frac{r}{n} \)): \[ \frac{0.07}{12} \approx 0.0058333333 \] 4. Add the periodic interest rate to 1: \[ 1 + 0.0058333333 \approx 1.0058333333 \] 5. Calculate the exponent (\( n \cdot t \)): \[ 12 \cdot 5 = 60 \] 6. Raise the base to the power of the exponent: \[ (1.0058333333)^{60} \approx 1.41758 \] 7. Multiply the principal amount by the result from the previous step: \[ 21,000 \cdot 1.41758 \approx 29770.1358 \] 8. Round the final answer to two decimal places: \[ 29770.1358 \approx 29770.13 \] Therefore, the future value of the investment is \$[/tex]29,770.13.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.