you deposit $10000 in an account earning 4% interest compounded monthly. how much will you have in 25 years? how much interest will you earn

What is

10000(1.0033333...)^300 ?

To calculate the final amount and interest earned, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

Given:
P = $10,000
r = 4% or 0.04 (converted to decimal)
n = 12 (compounded monthly)
t = 25 years

Let's substitute these values into the formula:

A = 10,000(1 + 0.04/12)^(12*25)

Now, we'll calculate the final amount:

A = 10,000(1 + 0.003333)^300
A = 10,000(1.003333)^300
A ≈ 10,000 * 2.208040
A ≈ $22,080.40

So, after 25 years, you will have approximately $22,080.40 in your account.

To calculate the interest earned, we can subtract the initial deposit from the final amount:

Interest = A - P
Interest = $22,080.40 - $10,000
Interest ≈ $12,080.40

Therefore, you will earn approximately $12,080.40 in interest over 25 years.

To calculate how much money you will have in 25 years and the amount of interest earned, we can use the formula for compound interest.

The formula for compound interest is:

A = P * (1 + r/n)^(n*t)

Where:
A = the future value of the account
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

In this case, you deposited $10,000 and the interest rate is 4% (or 0.04), compounded monthly (n = 12) for 25 years (t = 25).

Using the formula, we can calculate the future value of the account:

A = $10,000 * (1 + 0.04/12)^(12*25)
A = $10,000 * (1 + 0.003333)^300
A = $10,000 * (1.003333)^300
A ≈ $21,911.73

So, you will have approximately $21,911.73 in the account after 25 years.

To calculate the interest earned, you can subtract the initial deposit from the future value:

Interest = $21,911.73 - $10,000
Interest ≈ $11,911.73

Therefore, you will earn approximately $11,911.73 in interest over 25 years.