Final answer:
Mikey's investment with compound interest will grow exponentially as the interest is calculated on the accumulated balance, which includes both the initial principal and the previously earned interest.
Step-by-step explanation:
Mikey's investment in a savings account that applies compound interest weekly will grow exponentially, not linearly. This is because compound interest is interest that is earned on both the initial principal and the accumulated interest from previous periods. In the case of Mikey's savings, each week the interest for the next week is calculated on the total balance of the account, which includes the previous weeks' interest.
For example, if you start with $100 in an account with a 2% annual interest rate, after one year you'll have $102. This new amount will now be the base for the next year's interest calculation, leading to an amount of $104.04, and so on. The investment grows more quickly over time as the interest compounds. This is why the power of compound interest can lead to significant growth of an investment, especially if started early and allowed to grow over many years.
A formula commonly used to calculate the future value of an investment with compound interest is:
Future Value = Principal * (1 + interest rate)number of periods