What amount would you have if you deposited $2,500.00 a year for 30 years at 8 percent (compounded annually)?
To find the amount you would have after 30 years, let's break down the question and calculate it step by step.
First, we'll calculate the compounded interest for each year using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $2,500.00, the annual interest rate (r) is 8% (or 0.08 as a decimal), the number of times compounded per year (n) is 1 (annually), and the number of years (t) is 30.
Plugging these values into the formula, we get:
A = 2,500(1 + 0.08/1)^(1*30)
Simplifying further:
A = 2,500(1 + 0.08)^30
Now, let's calculate the final amount using a calculator or a spreadsheet software:
A = 2,500(1.08)^30
After evaluating this expression, we find that the amount would be approximately $24,783.89