Answer:
Meg will be able to spend approximately $259.16 on the new bike.
Explanation:
Using the formula A=P(1+r/n)^(n*t), where:
P = $200 (initial deposit)
r = 0.08 (8% interest rate expressed as a decimal)
n = 1 (compounded annually)
t = 3 (3 years)
A = 200(1 + 0.08/1)^(1*3) = 200(1.08)^3 ≈ $259.16
Therefore, Meg will be able to spend approximately $259.16 on the new bike.
Step by step (for more help):
Step 1: Identify the given information
Read the problem carefully and identify the relevant information. In this case, we are given that Meg deposited $200.00 into a savings account with an 8% annual interest rate, compounded annually. We are also told that she wants to use the money to buy a new bicycle in 3 years.
Step 2: Identify the formula to use
The formula for compound interest is A = P(1 + r/n)^(n*t), where:
A is the balance (final amount)
P is the principal (starting amount)
r is the interest rate expressed as a decimal
n is the number of times per year that the interest is compounded
t is the time in years
Since the interest is compounded annually in this problem, we will use n = 1.
Step 3: Plug in the values
Now we can plug in the values that we identified in Step 1 into the formula from Step 2.
A = P(1 + r/n)^(n*t)
A = 200(1 + 0.08/1)^(1*3)
Simplifying the right-hand side:
A = 200(1.08)^3
Step 4: Solve for the final amount
Using a calculator, we can evaluate the right-hand side to find the final amount:
A ≈ $259.16
Therefore, Meg will be able to spend approximately $259.16 on the new bike.
I hope this helps you understand how to approach compound interest problems. If you have any more questions, feel free to ask!
Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :}