Final answer:
To have $10,000 in ten years with an interest rate of 10% compounded annually, you would need to deposit approximately $3,854.84 in the bank account.
Step-by-step explanation:
To find out how much money you need to deposit now in order to have $10,000 in ten years with an interest rate of 10% compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value (amount of money you want to have)
- P is the principal (the initial amount of money you deposit)
- r is the interest rate (expressed as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
Plugging in the given values, we have:
10,000 = P(1 + 0.10/1)^(1 × 10)
Simplifying, we get:
10 = P(1.10^10)
Dividing both sides by 1.10^10, we get:
$10,000 / 1.10^10 = P
Calculating using a calculator, we find that P is approximately $3,854.84. Therefore, you would need to deposit $3,854.84 in the bank account to have $10,000 in ten years.