Monica wants to open a savings account with a deposit of \$1752. Monica will not make any additional deposits or withdrawals after she opens the account. Her bank offers two different savings accounts. - Account \( X \) pays \( 7.8 \% \) simple annual interest. - Account \( Y \) pays 8.9 interest compounded annually. Complete the statement about these two accounts after 7 years. Account \( Y \) would earn Monica about \( \$ \) \( \square \) 357.87 more interest than Account \( X \).
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Bonus Knowledge
To calculate the interest earned from both accounts, we can use the formulas for simple and compound interest. For Account \(X\) with simple interest: Interest \(I_X = P \times r \times t\) = \$1752 × 0.078 × 7 = \$960.96. For Account \(Y\) with compound interest: Amount \(A_Y = P(1 + r)^t\) = \$1752 × (1 + 0.089)^7 = \$1752 × (1.089)^7 ≈ \$1752 × 1.7461 ≈ \$3,058.23. Interest \(I_Y = A_Y - P\) = \$3,058.23 - \$1752 = \$1,306.23. Finally, calculating the difference: \$1,306.23 (Account Y) - \$960.96 (Account X) ≈ \$345.27. So, Account \(Y\) would earn Monica about \(\$ \square\) \(345.27\) more interest than Account \(X\). Can you believe how much compounding can work to your advantage? It’s like planting a tree; the more you nurture it, the bigger it grows! Speaking of gardening, did you know that understanding the power of compounding can help you make informed choices not just in finance but also in life? Just like the care you put into your finances, nurturing personal growth can lead to thriving results!
