A self-employed person deposit $3000 annually into a retirement account that earns 8% interest. How much will he have in 25 years?
To calculate the amount this self-employed person will have in their retirement account in 25 years, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years
In this case:
P = $3000 (annual deposit)
r = 8% per year (0.08 in decimal form)
n = 1 (compounded annually)
t = 25 years
So the formula becomes:
A = $3000(1 + 0.08/1)^(1*25)
Simplifying further:
A = $3000(1 + 0.08)^25
Calculating (1 + 0.08) first:
1 + 0.08 = 1.08
Now, we can substitute it back into the equation:
A = $3000(1.08)^25
Using a calculator, you can find that (1.08)^25 is approximately 3.1720418.
Therefore:
A ≈ $3000 * 3.1720418 ≈ $9,516.12
So, the self-employed person will have approximately $9,516.12 in their retirement account after 25 years.