Math / Algebra

QuestionCalculate the compound amount from the given data. principal $=\$ 650$ , compounded monthly, 11 years, annual rate $=6 \%$

Studdy Solution

STEP 1

1. The interest is compounded monthly, which means there are 12 compounding periods per year.
2. The principal amount is \$650.
3. The interest rate is 6% annually.
4. The time period for the investment is 11 years.
5. The compound amount formula is used: $ A = P \left(1 + \frac{r}{n}\right)^{nt} $, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

STEP 2

1. Identify and assign the given values to the variables in the compound interest formula.
2. Substitute the values into the compound interest formula.
3. Calculate the compound amount.

STEP 3

Identify and assign the given values to the variables in the compound interest formula.
$\begin{align} P & = 650 \\ r & = 0.06 \\ n & = 12 \\ t & = 11 \\ \end{align}$

STEP 4

Substitute the values into the compound interest formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$ .
$A = 650 \left(1 + \frac{0.06}{12}\right)^{12 \cdot 11}$

STEP 5

Calculate the term inside the parentheses first.
$1 + \frac{0.06}{12} = 1 + 0.005 = 1.005$

STEP 6

Calculate the exponent $12 \times 11$ .
$12 \times 11 = 132$

STEP 7

Raise the base $1.005$ to the power of 132.
$1.005^{132}$
Using a calculator, we find:
$1.005^{132} \approx 2.0156$

STEP 8

Multiply the result by the principal amount $\$650$ .
$A = 650 \times 2.0156 \approx 1,310.14$
Solution: The compound amount after 11 years is approximately \$1,310.14.

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QuestionCalculate the compound amount from the given data. principal $=\$ 650$ , compounded monthly, 11 years, annual rate $=6 \%$

Studdy Solution

STEP 1

STEP 2

1. Identify and assign the given values to the variables in the compound interest formula.
2. Substitute the values into the compound interest formula.
3. Calculate the compound amount.

STEP 3

Identify and assign the given values to the variables in the compound interest formula.
$\begin{align} P & = 650 \\ r & = 0.06 \\ n & = 12 \\ t & = 11 \\ \end{align}$

STEP 4

Substitute the values into the compound interest formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$ .
$A = 650 \left(1 + \frac{0.06}{12}\right)^{12 \cdot 11}$

STEP 5

Calculate the term inside the parentheses first.
$1 + \frac{0.06}{12} = 1 + 0.005 = 1.005$

STEP 6

Calculate the exponent $12 \times 11$ .
$12 \times 11 = 132$

STEP 7

Raise the base $1.005$ to the power of 132.
$1.005^{132}$
Using a calculator, we find:
$1.005^{132} \approx 2.0156$

STEP 8

Multiply the result by the principal amount $\$650$ .
$A = 650 \times 2.0156 \approx 1,310.14$
Solution: The compound amount after 11 years is approximately \$1,310.14.

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QuestionCalculate the compound amount from the given data. principal =$650=\$ 650=$650, compounded monthly, 11 years, annual rate =6%=6 \%=6%

Studdy Solution

STEP 1

STEP 2

1. Identify and assign the given values to the variables in the compound interest formula.2. Substitute the values into the compound interest formula.3. Calculate the compound amount.

STEP 3

Identify and assign the given values to the variables in the compound interest formula.P=650r=0.06n=12t=11 \begin{align*} P & = 650 \\ r & = 0.06 \\ n & = 12 \\ t & = 11 \\ \end{align*} Prnt​=650=0.06=12=11​

STEP 4

Substitute the values into the compound interest formula A=P(1+rn)nt A = P \left(1 + \frac{r}{n}\right)^{nt} A=P(1+nr​)nt.A=650(1+0.0612)12⋅11 A = 650 \left(1 + \frac{0.06}{12}\right)^{12 \cdot 11} A=650(1+120.06​)12⋅11

STEP 5

Calculate the term inside the parentheses first.1+0.0612=1+0.005=1.005 1 + \frac{0.06}{12} = 1 + 0.005 = 1.005 1+120.06​=1+0.005=1.005

STEP 6

Calculate the exponent 12×11 12 \times 11 12×11.12×11=132 12 \times 11 = 132 12×11=132

STEP 7

Raise the base 1.005 1.005 1.005 to the power of 132.1.005132 1.005^{132} 1.005132Using a calculator, we find:1.005132≈2.0156 1.005^{132} \approx 2.0156 1.005132≈2.0156

STEP 8

Multiply the result by the principal amount $650 \$650 $650.A=650×2.0156≈1,310.14 A = 650 \times 2.0156 \approx 1,310.14 A=650×2.0156≈1,310.14Solution: The compound amount after 11 years is approximately \$1,310.14.

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QuestionCalculate the compound amount from the given data. principal $=\$ 650$ , compounded monthly, 11 years, annual rate $=6 \%$

1. Identify and assign the given values to the variables in the compound interest formula.
2. Substitute the values into the compound interest formula.
3. Calculate the compound amount.

Identify and assign the given values to the variables in the compound interest formula.
$\begin{align} P & = 650 \\ r & = 0.06 \\ n & = 12 \\ t & = 11 \\ \end{align}$

Substitute the values into the compound interest formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$ .
$A = 650 \left(1 + \frac{0.06}{12}\right)^{12 \cdot 11}$

Calculate the term inside the parentheses first.
$1 + \frac{0.06}{12} = 1 + 0.005 = 1.005$

Calculate the exponent $12 \times 11$ .
$12 \times 11 = 132$

Raise the base $1.005$ to the power of 132.
$1.005^{132}$
Using a calculator, we find:
$1.005^{132} \approx 2.0156$

Multiply the result by the principal amount $\$650$ .
$A = 650 \times 2.0156 \approx 1,310.14$
Solution: The compound amount after 11 years is approximately \$1,310.14.