Suppose \( \$ 3,900 \) is deposited into an account which has an annual percentage rate of \( 7.77 \% \) per year. Assume it remains in the account for 22 years and no additional money is added to the account other than interest. (a) Complete the boxes below to write an expression for the amount (in dollars) at year \( x=22 \), of assuming interest is compounded annually. Do not round any values. You can enter arithmetic expressions (containing \( +,-,{ }^{*}, / \, or \wedge \) ) in any of these boxes. 22 \( \square \) \[ 3900 \] - ( \( 1+0.0777 \) ) What is the value in year \( x=22 \) of an investment of \( \$ 3,900 \) dollars which pays \( 7.77 \% \) compounded annually? \$ \( \square \) 20,231.03 (Round to the nearest 0.01 dollars)
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To dive deeper into the world of compound interest, it’s fascinating to note that the concept dates back to ancient civilizations. The Babylonians were among the first to calculate interest, and they recognized the power of compounding over time. By the late Middle Ages, interest calculations had evolved, leading to the modern financial systems we use today, paving the way for everything from savings accounts to investment portfolios. Now, let’s talk about practical applications! Understanding how compound interest works can completely change your approach to saving and investing. For example, if you start investing early in a retirement account with a good interest rate, the compounding can significantly grow your wealth over decades. This is particularly crucial for young savers; even small monthly contributions can snowball into a substantial nest egg thanks to the magical effect of compounding interest!
