We can solve this problem using the formula for compound interest:
\[A = P\left(1 + \frac{r}{n}\right)^{n\cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12%
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Plugging in the values, we have:
\[A = 70\left(1 + \frac{0.12}{12}\right)^{12\cdot \frac{2}{12}}\]
Simplifying within the parentheses:
\[A = 70\left(1 + \frac{0.01}{12}\right)^{2}\]
\[A = 70\left(1 + 0.000833\right)^{2}\]
And finally, calculating the power:
\[A = 70(1.000833)^{2}\]
\[A \approx 70(1.001666)\]
\[A \approx \boxed{70.12}\]
When $70 is invested monthly with an annual compound interest rate of 12% interest, compounded monthly, what is the total amount of the investment at the end of the second month? Round the answer to two decimal places as needed.(1 point)?
7 answers
thats incorrect
I apologize for the mistake in my previous response. Let's go through the solution again.
The formula for compound interest is:
\[A = P\left(1 + \frac{r}{n}\right)^{n\cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12% or 0.12
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Using these values, we have:
\[A = 70\left(1 + \frac{0.12}{12}\right)^{12\cdot \frac{2}{12}}\]
\[A = 70\left(1 + 0.01\right)^{2}\]
\[A = 70(1.01)^{2}\]
\[A = 70(1.0201)\]
\[A \approx \boxed{71.41}\]
Therefore, the total amount of the investment at the end of the second month is approximately $71.41.
The formula for compound interest is:
\[A = P\left(1 + \frac{r}{n}\right)^{n\cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12% or 0.12
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Using these values, we have:
\[A = 70\left(1 + \frac{0.12}{12}\right)^{12\cdot \frac{2}{12}}\]
\[A = 70\left(1 + 0.01\right)^{2}\]
\[A = 70(1.01)^{2}\]
\[A = 70(1.0201)\]
\[A \approx \boxed{71.41}\]
Therefore, the total amount of the investment at the end of the second month is approximately $71.41.
wrong
I apologize for the mistake in my previous responses. Let's go through the solution again.
The formula for compound interest is:
\[A = P\left(1 + \frac{r}{n}\right)^{n\cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12% or 0.12
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Using these values, we have:
\[A = 70\left(1 + \frac{0.12}{12}\right)^{12\cdot \frac{2}{12}}\]
\[A = 70\left(1 + \frac{0.01}{12}\right)^{2}\]
\[A = 70\left(1 + 0.000833\right)^{2}\]
\[A = 70(1.000833)^{2}\]
\[A \approx 70(1.001666)\]
\[A \approx \boxed{70.12}\]
Therefore, the total amount of the investment at the end of the second month is approximately $70.12.
The formula for compound interest is:
\[A = P\left(1 + \frac{r}{n}\right)^{n\cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12% or 0.12
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Using these values, we have:
\[A = 70\left(1 + \frac{0.12}{12}\right)^{12\cdot \frac{2}{12}}\]
\[A = 70\left(1 + \frac{0.01}{12}\right)^{2}\]
\[A = 70\left(1 + 0.000833\right)^{2}\]
\[A = 70(1.000833)^{2}\]
\[A \approx 70(1.001666)\]
\[A \approx \boxed{70.12}\]
Therefore, the total amount of the investment at the end of the second month is approximately $70.12.
wrong again
I apologize for the errors in my previous responses. Let's try solving the problem again.
The formula for compound interest is:
\[A = P \left(1 + \frac{r}{n}\right)^{n \cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12% or 0.12
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Using these values, we have:
\[A = 70 \left(1 + \frac{0.12}{12}\right)^{12 \cdot \frac{2}{12}}\]
Simplifying within the parentheses:
\[A = 70 \left(1 + 0.01\right)^{2}\]
\[A = 70 \cdot 1.01^{2}\]
Calculating the power:
\[A = 70 \cdot 1.0201\]
\[A \approx \boxed{71.41}\]
Therefore, the total amount of the investment at the end of the second month is approximately $71.41.
The formula for compound interest is:
\[A = P \left(1 + \frac{r}{n}\right)^{n \cdot t}\]
Where:
- $A$ is the total amount of the investment at the end of the second month
- $P$ is the principal amount, which is $70
- $r$ is the annual interest rate, which is 12% or 0.12
- $n$ is the number of times the interest is compounded per year, which is monthly and therefore 12
- $t$ is the total investment period in years, which is 2 months and therefore $\frac{2}{12}$
Using these values, we have:
\[A = 70 \left(1 + \frac{0.12}{12}\right)^{12 \cdot \frac{2}{12}}\]
Simplifying within the parentheses:
\[A = 70 \left(1 + 0.01\right)^{2}\]
\[A = 70 \cdot 1.01^{2}\]
Calculating the power:
\[A = 70 \cdot 1.0201\]
\[A \approx \boxed{71.41}\]
Therefore, the total amount of the investment at the end of the second month is approximately $71.41.
1 answer