Final answer:
To have $10,000 in ten years in a bank account that pays 10% interest compounded annually, you need to put in $3,854.91.
Step-by-step explanation:
To find out how much money you have to put into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, you can use the compound interest formula. The formula is:
A = P(1 + r/n)^(nt)
Where A is the future value, P is the principal (the initial amount of money), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we know that the future value (A) is $10,000, the annual interest rate (r) is 0.10, and the number of years (t) is 10. We need to solve for the principal (P).
Plugging in the values into the formula:
$10,000 = P(1 + 0.10/1)^(1*10)
$10,000 = P(1.10)^10
Dividing both sides of the equation by (1.10)^10:
P = $10,000 / (1.10)^10
P = $10,000 / 2.5937
P = $3,854.91