You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 35 years?

You deposit $3000 each year into an account earning 5% interest compounded annually. How much will you have in the account in 30 years?

Well, well, well! You've just stepped into the world of finance. Let me entertain you with some fun calculations!

So, you deposit $3000 each year for 35 years at an interest rate of 7% compounded annually. Now, let's do some math magic!

The formula for compound interest is:

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

Where:
A = the amount of money you'll have in the account after 35 years
P = your initial deposit of $3000
r = the interest rate of 7% (converted to decimal, it's 0.07)
n = number of times the interest is compounded per year (since it's compounded annually, n = 1)
t = number of years (in this case, t = 35)

So, when we plug in all the numbers and calculate, we get:

A = 3000(1 + 0.07/1)^(1*35)

Calculating further, we have:

A ≈ $24,048.79

Voila! After the magic of compound interest, you'll have approximately $24,048.79 in your account. Keep in mind, though, that this number doesn't account for any additional deposits made after the 35 years.

To find out how much you will have in the account in 35 years, you can use the formula for compound interest:

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

where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

In this case, you deposit $3000 each year, so the principal investment amount is $3000. The interest rate is 7%, which in decimal form is 0.07. The interest is compounded annually, so n = 1. The investment period is 35 years, so t = 35.

Plugging in these values into the formula, we can calculate the future value (A):

A = $3000(1 + 0.07/1)^(1*35)

Solving this equation step by step:

A = $3000(1 + 0.07)^(35)
A = $3000(1.07)^(35)
A ≈ $3000(5.586414)
A ≈ $16,759.24

Therefore, you will have approximately $16,759.24 in the account after 35 years.

To calculate the future value of the account, we can use the formula for compound interest:

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

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

In this case, the principal amount (P) is $3000, the annual interest rate (r) is 7% (or 0.07 as a decimal), the interest is compounded annually (n = 1), and the duration (t) is 35 years.

Substituting these values into the formula:

A = 3000(1 + 0.07/1)^(1*35)

Now, let's calculate it step by step:

Step 1: Calculate the exponent part of the equation:
(1 + 0.07/1)^(1*35) = 1.07^35

Step 2: Raise 1.07 to the power of 35:
1.07^35 ≈ 7.612320041

Step 3: Multiply the result from step 2 by the principal amount:
3000 * 7.612320041 ≈ 22,836.96

Therefore, after 35 years, you would have approximately $22,836.96 in the account.

3000 [ 1.07^35 - 1 ] / 0.07

= 3000 [ 10.68 -1] /.07

= 3000 * 138

= 414,710.64