QuestionInvest \$6000 at 4\% for 5 years, compounded semiannually. Find the amount after 5 years (round to nearest cent).

Studdy Solution

STEP 1

Assumptions1. The principal amount is \$6000. The annual interest rate is4%
3. The time for compounding is5 years4. The interest is compounded semiannually

STEP 2

The formula for compound interest is given by $A = \left(1 + \frac{r}{n}\right)^{nt}$ where- A is the amount of money accumulated after n years, including interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal). - n is the number of times that interest is compounded per year. - t is the time the money is invested for in years.

STEP 3

First, we need to convert the annual interest rate from a percentage to a decimal. We do this by dividing the percentage by100.
$r = \frac{\%}{100} =0.04$

STEP 4

Now, we need to identify the number of times the interest is compounded per year. Since it is compounded semiannually, this means it is compounded twice a year.
$n =2$

STEP 5

Substitute the values of, r, n and t into the formula.
$A = \$6000 \left(1 + \frac{0.04}{2}\right)^{2 \times5}$

STEP 6

Calculate the amount in the account after5 years.
$A = \$6000 \left(1 +0.02\right)^{10}$

STEP 7

implify the expression inside the parentheses.
$A = \$6000 \times (1.02)^{10}$

STEP 8

Calculate the final amount.
$A = \$6000 \times (1.02)^{10} = \$7298.63$ The amount in the account after5 years if the account is compounded semiannually is \$7298.63.

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QuestionInvest \$6000 at 4\% for 5 years, compounded semiannually. Find the amount after 5 years (round to nearest cent).

Studdy Solution

STEP 1

Assumptions1. The principal amount is \$6000. The annual interest rate is4%
3. The time for compounding is5 years4. The interest is compounded semiannually

STEP 2

STEP 3

First, we need to convert the annual interest rate from a percentage to a decimal. We do this by dividing the percentage by100.
$r = \frac{\%}{100} =0.04$

STEP 4

Now, we need to identify the number of times the interest is compounded per year. Since it is compounded semiannually, this means it is compounded twice a year.
$n =2$

STEP 5

Substitute the values of, r, n and t into the formula.
$A = \$6000 \left(1 + \frac{0.04}{2}\right)^{2 \times5}$

STEP 6

Calculate the amount in the account after5 years.
$A = \$6000 \left(1 +0.02\right)^{10}$

STEP 7

implify the expression inside the parentheses.
$A = \$6000 \times (1.02)^{10}$

STEP 8

Calculate the final amount.
$A = \$6000 \times (1.02)^{10} = \$7298.63$ The amount in the account after5 years if the account is compounded semiannually is \$7298.63.

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QuestionInvest \$6000 at 4\% for 5 years, compounded semiannually. Find the amount after 5 years (round to nearest cent).

Studdy Solution

STEP 1

Assumptions1. The principal amount is \$6000. The annual interest rate is4%3. The time for compounding is5 years4. The interest is compounded semiannually

STEP 2

STEP 3

First, we need to convert the annual interest rate from a percentage to a decimal. We do this by dividing the percentage by100.r=%100=0.04r = \frac{\%}{100} =0.04r=100%​=0.04

STEP 4

Now, we need to identify the number of times the interest is compounded per year. Since it is compounded semiannually, this means it is compounded twice a year.n=2n =2n=2

STEP 5

Substitute the values of, r, n and t into the formula.A=$6000(1+0.042)2×5A = \$6000 \left(1 + \frac{0.04}{2}\right)^{2 \times5}A=$6000(1+20.04​)2×5

STEP 6

Calculate the amount in the account after5 years.A=$6000(1+0.02)10A = \$6000 \left(1 +0.02\right)^{10}A=$6000(1+0.02)10

STEP 7

implify the expression inside the parentheses.A=$6000×(1.02)10A = \$6000 \times (1.02)^{10}A=$6000×(1.02)10

STEP 8

Calculate the final amount.A=$6000×(1.02)10=$7298.63A = \$6000 \times (1.02)^{10} = \$7298.63A=$6000×(1.02)10=$7298.63The amount in the account after5 years if the account is compounded semiannually is \$7298.63.

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

Assumptions1. The principal amount is \$6000. The annual interest rate is4%
3. The time for compounding is5 years4. The interest is compounded semiannually

First, we need to convert the annual interest rate from a percentage to a decimal. We do this by dividing the percentage by100.
$r = \frac{\%}{100} =0.04$

Now, we need to identify the number of times the interest is compounded per year. Since it is compounded semiannually, this means it is compounded twice a year.
$n =2$

Substitute the values of, r, n and t into the formula.
$A = \$6000 \left(1 + \frac{0.04}{2}\right)^{2 \times5}$

Calculate the amount in the account after5 years.
$A = \$6000 \left(1 +0.02\right)^{10}$

implify the expression inside the parentheses.
$A = \$6000 \times (1.02)^{10}$

Calculate the final amount.
$A = \$6000 \times (1.02)^{10} = \$7298.63$ The amount in the account after5 years if the account is compounded semiannually is \$7298.63.