Final answer:
To have $10,000 in ten years with a 10% interest rate compounded annually, you would need to put approximately $3,858.09 into the bank account.
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the principal (the initial amount)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the final amount A is $10,000, the annual interest rate r is 10% (0.10 in decimal form), the number of times interest is compounded per year n is 1 (annually), and the number of years t is 10.
Plugging these values into the formula:
$10,000 = P(1 + 0.10/1)^(1*10)
Simplifying the equation:
$10,000 = P(1.10)^10
To find the principal P, we can divide both sides of the equation by (1.10)^10:
P = $10,000 / (1.10)^10
Using a calculator to evaluate (1.10)^10, we find:
P = $10,000 / 2.5937
P ≈ $3,858.09
Therefore, you would need to put approximately $3,858.09 into the bank account to have $10,000 in ten years.