Final answer:
To have $10,000 in ten years in an account with a 10% annual interest rate, compounded annually, you need to deposit approximately $3,855.43 today.
Step-by-step explanation:
To calculate the amount of money you need to deposit into an account with a 10% annual interest rate to have $10,000 in ten years, you can use the formula for compound interest. The formula is P = A / (1+r)ⁿ, where P is the principal amount (the initial amount of money), A is the future value of the investment/loan, including interest, r is the annual interest rate (decimal), and n is the number of years the money is invested or borrowed for.
First, we must convert the interest rate from a percentage to a decimal, which is done by dividing by 100. So, the annual interest rate is 0.10. Using the formula, we substitute the known values:
P = $10,000 / (1+0.10)¹⁰
Now, calculate the denominator:
(1+0.10)^10 = 1.10¹⁰ ≈ 2.59374
Then, divide the future value by this amount to find the initial deposit:
P = $10,000 / 2.59374 ≈ $3,855.43
Therefore, you would need to deposit approximately $3,855.43 today in your bank account to have $10,000 in ten years, assuming the interest is compounded annually at a rate of 10%.