Math / Algebra

QuestionFind total amount in the componnd intest account 1100 is compound remiennally at a rate of 7 is fre 20 yeurs

Studdy Solution

STEP 1

1. The principal amount (initial investment) is $1100.
2. The interest rate is 7% per annum.
3. The interest is compounded semiannually.
4. The time period for the investment is 20 years.
5. We are trying to find the total amount in the account after 20 years.

STEP 2

1. Understand the formula for compound interest.
2. Identify the values of the variables in the formula.
3. Substitute the values into the formula.
4. Calculate the total amount.

STEP 3

Understand the formula for compound interest. The formula is:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$
where: - $A$ is the total amount after time $t$ , - $P$ is the principal amount, - $r$ is the annual interest rate (decimal), - $n$ is the number of times interest is compounded per year, - $t$ is the time in years.

STEP 4

Identify the values of the variables in the formula: - $P = 1100$ - $r = 0.07$ (7% as a decimal) - $n = 2$ (since interest is compounded semiannually) - $t = 20$

STEP 5

Substitute the values into the formula:
$A = 1100 \left(1 + \frac{0.07}{2}\right)^{2 \times 20}$

STEP 6

Calculate the total amount:
First, calculate the expression inside the parentheses:
$1 + \frac{0.07}{2} = 1 + 0.035 = 1.035$
Now calculate the exponent:
$2 \times 20 = 40$
Substitute these into the formula:
$A = 1100 \times (1.035)^{40}$
Calculate $(1.035)^{40}$ using a calculator:
$(1.035)^{40} \approx 3.8697$
Finally, calculate the total amount $A$ :
$A = 1100 \times 3.8697 \approx 4256.67$
The total amount in the compound interest account after 20 years is approximately:
$\boxed{4256.67}$

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QuestionFind total amount in the componnd intest account 1100 is compound remiennally at a rate of 7 is fre 20 yeurs

Studdy Solution

STEP 1

1. The principal amount (initial investment) is $1100.
2. The interest rate is 7% per annum.
3. The interest is compounded semiannually.
4. The time period for the investment is 20 years.
5. We are trying to find the total amount in the account after 20 years.

STEP 2

1. Understand the formula for compound interest.
2. Identify the values of the variables in the formula.
3. Substitute the values into the formula.
4. Calculate the total amount.

STEP 3

STEP 4

Identify the values of the variables in the formula: - $P = 1100$ - $r = 0.07$ (7% as a decimal) - $n = 2$ (since interest is compounded semiannually) - $t = 20$

STEP 5

Substitute the values into the formula:
$A = 1100 \left(1 + \frac{0.07}{2}\right)^{2 \times 20}$

STEP 6

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QuestionFind total amount in the componnd intest account 1100 is compound remiennally at a rate of 7 is fre 20 yeurs

Studdy Solution

STEP 1

1. The principal amount (initial investment) is $1100.2. The interest rate is 7% per annum.3. The interest is compounded semiannually.4. The time period for the investment is 20 years.5. We are trying to find the total amount in the account after 20 years.

STEP 2

1. Understand the formula for compound interest.2. Identify the values of the variables in the formula.3. Substitute the values into the formula.4. Calculate the total amount.

STEP 3

STEP 4

Identify the values of the variables in the formula: - P=1100 P = 1100 P=1100 - r=0.07 r = 0.07 r=0.07 (7% as a decimal) - n=2 n = 2 n=2 (since interest is compounded semiannually) - t=20 t = 20 t=20

STEP 5

Substitute the values into the formula:A=1100(1+0.072)2×20 A = 1100 \left(1 + \frac{0.07}{2}\right)^{2 \times 20} A=1100(1+20.07​)2×20

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The principal amount (initial investment) is $1100.
2. The interest rate is 7% per annum.
3. The interest is compounded semiannually.
4. The time period for the investment is 20 years.
5. We are trying to find the total amount in the account after 20 years.

1. Understand the formula for compound interest.
2. Identify the values of the variables in the formula.
3. Substitute the values into the formula.
4. Calculate the total amount.

Identify the values of the variables in the formula: - $P = 1100$ - $r = 0.07$ (7% as a decimal) - $n = 2$ (since interest is compounded semiannually) - $t = 20$

Substitute the values into the formula:
$A = 1100 \left(1 + \frac{0.07}{2}\right)^{2 \times 20}$