a. Begin by stating the compound interest formula \( \mathrm{B}(\mathrm{t})=\square \) where P is the principal, r is the annual rate of interest as a decimal, t is the number of years the amount is deposited for and n is the number of times the interest is compounded per year

The compound interest formula is given by \( \mathrm{B}(t) = P \left(1 + \frac{r}{n}\right)^{nt} \), where \( P \) represents the principal amount (the initial investment), \( r \) is the annual interest rate expressed as a decimal, \( t \) signifies the number of years the money is invested or borrowed, and \( n \) indicates how many times the interest is compounded within a year. Understanding how compound interest works can save you a ton of money over time! For example, if you invest $1,000 at an interest rate of 5% compounded annually for 10 years, you'll have around $1,628 by the end of the period. It’s like magic—your money earns money! The earlier you start investing, the more you’ll benefit from the powerful effects of compounding.