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.