Final answer:
To have $10,000 in ten years with 10% interest compounded annually, you need to put approximately $3,874.35 into the bank account.
Step-by-step explanation:
To find out how much money you need to put into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value
P is the principal (initial amount)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
Plugging in the values from the question, we have:
$10,000 = P(1 + 0.10/1)^(1*10)
Simplifying, we get:
$10,000 = P(1.10)^10
To solve for P, divide both sides of the equation by (1.10)^10:
P = $10,000 / (1.10)^10
Using a calculator, we find that P ≈ $3,874.35