Final answer:
Andrea needs to deposit approximately $3,855.43 into a bank account with a 10% annual interest rate, compounded annually, to have $10,000 in ten years.
Step-by-step explanation:
In order to determine how much money Andrea needs to deposit into a bank account that pays 10% interest compounded annually 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 for, in years.
We need to rearrange this formula to solve for P when A is $10,000, r is 10% (or 0.10 as a decimal), n is 1 (since it's compounded annually), and t is 10 years.
So the rearranged formula to solve for P is:
P = A / (1 + r/n)^(nt)
Substituting the values we get:
P = $10,000 / (1 + 0.10/1)^(1*10)
P = $10,000 / (1.10)^10
P = $10,000 / 2.59374
P = $3,855.43 (approximately)
This means Andrea would need to deposit approximately $3,855.43 in a bank account today to have $10,000 in ten years with a 10% interest rate compounded annually.