QuestionIf \$24 was invested at 3\% annual interest from 1626 to 2020, how much is in the account now? Round to the nearest dollar.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $24. The annual interest rate is3%
3. The interest is compounded annually4. The time period is from1626 to2020, which is394 years

STEP 2

We can use the formula for compound interest to calculate the final amount in the account. The formula is $A = \left(1 + \frac{r}{n}\right)^{nt}$ 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

Since the interest is compounded annually, $n$ is1. So, the formula simplifies to $A = \left(1 + r\right)^t$

STEP 4

Now, plug in the given values for the principal amount, interest rate, and time to calculate the final amount.
$A = \$24 \left(1 +3\%\right)^{394}$

STEP 5

Convert the percentage to a decimal value.
$3\% =0.03$ $A = \$24 \left(1 +0.03\right)^{394}$

STEP 6

Calculate the final amount.
$A = \$24 \left(1.03\right)^{394}$ This calculation may require a calculator with the ability to handle large exponents.

STEP 7

The final amount in the account is $A = \$24 \left(1.03\right)^{394} \approx \$7,646,787,261$ So, there would be about $7,646,787,261 in the account. Round to the nearest dollar as needed.

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QuestionIf \$24 was invested at 3\% annual interest from 1626 to 2020, how much is in the account now? Round to the nearest dollar.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $24. The annual interest rate is3%
3. The interest is compounded annually4. The time period is from1626 to2020, which is394 years

STEP 2

STEP 3

Since the interest is compounded annually, $n$ is1. So, the formula simplifies to $A = \left(1 + r\right)^t$

STEP 4

Now, plug in the given values for the principal amount, interest rate, and time to calculate the final amount.
$A = \$24 \left(1 +3\%\right)^{394}$

STEP 5

Convert the percentage to a decimal value.
$3\% =0.03$ $A = \$24 \left(1 +0.03\right)^{394}$

STEP 6

Calculate the final amount.
$A = \$24 \left(1.03\right)^{394}$ This calculation may require a calculator with the ability to handle large exponents.

STEP 7

The final amount in the account is $A = \$24 \left(1.03\right)^{394} \approx \$7,646,787,261$ So, there would be about $7,646,787,261 in the account. Round to the nearest dollar as needed.

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QuestionIf \$24 was invested at 3\% annual interest from 1626 to 2020, how much is in the account now? Round to the nearest dollar.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $24. The annual interest rate is3%3. The interest is compounded annually4. The time period is from1626 to2020, which is394 years

STEP 2

STEP 3

Since the interest is compounded annually, nnn is1. So, the formula simplifies toA=(1+r)tA = \left(1 + r\right)^tA=(1+r)t

STEP 4

Now, plug in the given values for the principal amount, interest rate, and time to calculate the final amount.A=$24(1+3%)394A = \$24 \left(1 +3\%\right)^{394}A=$24(1+3%)394

STEP 5

Convert the percentage to a decimal value.3%=0.033\% =0.033%=0.03A=$24(1+0.03)394A = \$24 \left(1 +0.03\right)^{394}A=$24(1+0.03)394

STEP 6

Calculate the final amount.A=$24(1.03)394A = \$24 \left(1.03\right)^{394}A=$24(1.03)394This calculation may require a calculator with the ability to handle large exponents.

STEP 7

The final amount in the account isA=$24(1.03)394≈$7,646,787,261A = \$24 \left(1.03\right)^{394} \approx \$7,646,787,261A=$24(1.03)394≈$7,646,787,261So, there would be about $7,646,787,261 in the account. Round to the nearest dollar as needed.

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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 initial amount (principal) is $24. The annual interest rate is3%
3. The interest is compounded annually4. The time period is from1626 to2020, which is394 years

Since the interest is compounded annually, $n$ is1. So, the formula simplifies to $A = \left(1 + r\right)^t$

Now, plug in the given values for the principal amount, interest rate, and time to calculate the final amount.
$A = \$24 \left(1 +3\%\right)^{394}$

Convert the percentage to a decimal value.
$3\% =0.03$ $A = \$24 \left(1 +0.03\right)^{394}$

Calculate the final amount.
$A = \$24 \left(1.03\right)^{394}$ This calculation may require a calculator with the ability to handle large exponents.

The final amount in the account is $A = \$24 \left(1.03\right)^{394} \approx \$7,646,787,261$ So, there would be about $7,646,787,261 in the account. Round to the nearest dollar as needed.