Final answer:
To have $10,000 in ten years with a 10% annual compound interest rate, one needs to deposit approximately $3855.43 today.
Step-by-step explanation:
To find out how much money needs to be deposited in a bank account with an annual compound interest rate of 10% to have $10,000 in ten years, we can use the formula for compound interest. The formula is A = P(1 + r/n)nt, where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
Since the interest is compounded annually, n is 1. We want A to be $10,000 after 10 years. Rearranging the formula to solve for P, we get P = A / (1 + r)t.
Substituting the given values:
P = $10,000 / (1 + 0.10)10
P = $10,000 / (1 + 0.10)10
P = $10,000 / (1.10)10
P = $10,000 / 2.59374
P = $3855.43 approximately
Therefore, the amount of money you need to deposit now to have $10,000 in ten years with a 10% annual compound interest is approximately $3855.43.