Question

You have been depositing money into a savings account on every birthday since your first (that is, when you turned one). The account pays an interest rate of ________?

1) 0%
2) 2%
3) 5%
4) 10%

Answer 1

To determine the initial deposit needed for an account with 10% compounded interest to reach $10,000 in 10 years, we use the formula A = P(1 + r)^t. By rearranging it for P, we find the required starting principal.

Step-by-step explanation:

The question asks us to calculate how much money needs to be deposited into a bank account with a 10% annual compounded interest rate to accumulate to $10,000 in 10 years. To find this, we can use the formula for compound interest which 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, and t is the time the money is invested for in years.

Since we want to have $10,000 in 10 years and the interest is compounded annually (n = 1), the formula simplifies to A = P(1 + r)t. We are solving for P here, and we know that A is $10,000, r is 0.10 (10% interest), and t is 10 years. Rearranging the formula to solve for P gives us P = A / (1 + r)t. Plugging in the numbers, we get P = $10,000 / (1 + 0.10)10, which will give us the initial deposit required to reach the $10,000 goal after 10 years.