To solve this problem, we can use the formula for continuous compound interest, which is A = P * e^(rt), where:

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time the money is invested for, in years.

Given in the problem:

- P = $2,500
- r = 12% = 0.12
- t = 3 years

Substitute these values into the formula:

A = 2500 * e^(0.12*3)

Now, calculate the exponent first:

0.12 * 3 = 0.36

So, the equation becomes:

A = 2500 * e^0.36

Now, use the value of e (approximately equal to 2.71828) and raise it to the power of 0.36:

e^0.36 ≈ 1.433127

So, the equation becomes:

A = 2500 * 1.433127

Finally, multiply 2500 by 1.433127 to get the total amount:

A ≈ 2500 * 1.433127 = $3582.82

So, the account balance after 3 years would be approximately $3582.82, assuming no additional deposits or withdrawals are made.

Question

To solve this problem, we can use the formula for continuous compound interest, which is A = P * e^(rt), where:

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time the money is invested for, in years.

Given in the problem:

- P = $2,500
- r = 12% = 0.12
- t = 3 years

Substitute these values into the formula:

A = 2500 * e^(0.12*3)

Now, calculate the exponent first:

0.12 * 3 = 0.36

So, the equation becomes:

A = 2500 * e^0.36

Now, use the value of e (approximately equal to 2.71828) and raise it to the power of 0.36:

e^0.36 ≈ 1.433127

So, the equation becomes:

A = 2500 * 1.433127

Finally, multiply 2500 by 1.433127 to get the total amount:

A ≈ 2500 * 1.433127 = $3582.82

So, the account balance after 3 years would be approximately $3582.82, assuming no additional deposits or withdrawals are made.

Knowee AI · Accepted Answer

To solve this problem, we can use the formula for continuous compound interest, which is A = P * e^(rt), where:

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time the money is invested for, in years.

Given in the problem:

- P = $2,500
- r = 12% = 0.12
- t = 3 years

Substitute these values into the formula:

A = 2500 * e^(0.12*3)

Now, calculate the exponent first:

0.12 * 3 = 0.36

So, the equation becomes:

A = 2500 * e^0.36

Now, use the value of e (approximately equal to 2.71828) and raise it to the power of 0.36:

e^0.36 ≈ 1.433127

So, the equation becomes:

A = 2500 * 1.433127

Finally, multiply 2500 by 1.433127 to get the total amount:

A ≈ 2500 * 1.433127 = $3582.82

So, the account balance after 3 years would be approximately $3582.82, assuming no additional deposits or withdrawals are made.

If $2,500 is invested at 12% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?

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