Final answer:
To determine how much Britney should deposit at the end of the summer, we can use the formula for compound interest. By plugging in the values, we can find that Britney should deposit approximately $9,393.65.
Step-by-step explanation:
To find out how much Britney should deposit at the end of the summer, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. Since Britney wants to have $10,000 by the time she's 21, which is approximately 3 years, we can plug in the values into the formula.
Let's assume Britney will deposit x amount of money at the end of the summer. So, P = x. The annual interest rate is 3.5%, which can be written as 0.035 in decimal form. The interest is compounded monthly, so n = 12. And t = 3.
Plugging in the values, we get: 10000 = x(1 + 0.035/12)^(12*3).
Simplifying the equation, we get: 10000 = x(1.00291666)^36.
Dividing both sides of the equation by (1.00291666)^36, we get: x = 10000 / (1.00291666)^36. Evaluating this expression gives us approximately x = $9,393.65.
Therefore, Britney should deposit approximately $9,393.65 at the end of the summer.