You deposit $3000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 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 amount (the initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

Given:
P = $3000 (annual deposit)
r = 2% = 0.02 (annual interest rate)
n = 1 (compounded annually)
t = 35 years

Plugging in these values into the formula:

A = $3000(1 + 0.02/1)^(1*35)

Simplifying the expression inside the parentheses:

A = $3000(1 + 0.02)^(35)

Calculating the values inside the parentheses:

A = $3000(1.02)^(35)

Calculating the exponential term using a calculator:

A ≈ $3000(1.8597)

Finally, calculating the future value of the account:

A ≈ $5579.10

Therefore, you will have approximately $5579.10 in the account after 35 years, considering the annual deposit of $3000 with a 2% interest rate compounded annually.

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

Future Value = Principal * (1 + Interest Rate)^Time

Where:
- Principal is the initial deposit
- Interest Rate is the annual interest rate in decimal form
- Time is the number of compounding periods

In this case, the principal is $3000, the interest rate is 2% (or 0.02 in decimal form), and the time is 35 years.

First, let's calculate the future value of the annual deposits using the formula for the future value of an ordinary annuity:

Future Value of Annuity = Annual Deposit * [(1 + Interest Rate)^Time - 1] / Interest Rate

Using this formula, the future value of the annual deposits after 35 years can be calculated as follows:

Future Value of Annuity = $3000 * [(1 + 0.02)^35 - 1] / 0.02

Simplifying this equation:

Future Value of Annuity = $3000 * [(1.02)^35 - 1] / 0.02

Now, let's calculate the future value of the initial deposit after 35 years using the compound interest formula:

Future Value of Principal = Principal * (1 + Interest Rate)^Time

Future Value of Principal = $3000 * (1 + 0.02)^35

Combining the future value of the annuity and the future value of the principal, we can calculate the total amount in the account after 35 years:

Total Future Value = Future Value of Annuity + Future Value of Principal

Total Future Value = $3000 * [(1.02)^35 - 1] / 0.02 + $3000 * (1 + 0.02)^35

Calculating this expression will give you the final amount you will have in the account after 35 years.

Use the annuity/compound interest formula.

FV=Future value
A=amount deposited each period = 3000
R=1+interest per period (year)=1.02
n=number years money was deposited
FV=A(1+R+R^2+...+R^(n-1)
=A(R^n-1)/(R-1)
Take out your calculator and find FV.
It should be around 150000.