Riley invests $100 in the year 2000. The account is compounded annually. The account earns 3% interest for a period of 30 years.
After 30 years, how much money will be in the account?
A = 100 * (1 + .03)^30
To calculate the amount of money in the account after 30 years with an annual compound interest of 3%, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case,
P = $100
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 30
Substituting the given values into the formula:
A = 100(1 + 0.03/1)^(1*30)
Now, we can simplify the calculation step by step:
A = 100(1 + 0.03)^(30)
A = 100(1.03)^(30)
Using a calculator or spreadsheet, we can calculate the value of (1.03)^30 to get:
A ≈ 100(1.435) ≈ $143.50
Therefore, after 30 years, there will be approximately $143.50 in Riley's account.