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Jarvis deposits of \( \$ 2500 \) into each of two savings accounts - Account I pays \( 5 \% \) simple annuat interest. - Account II pays 98 interest compounded annually, If Jarvis does not make any additionat deposits or withdrawals, what is the sum of the balances in Account and Account II at the end of 9 year?

Ask by Carrillo Elliott. in the United States
Mar 12,2025

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Answer

The total balance in both accounts after 9 years is approximately \$1,172,927.08.

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The Deep Dive

To calculate the balances in each account after 9 years, we'll use the formulas for simple interest for Account I and compound interest for Account II. For Account I, the formula for simple interest is: \[ A = P(1 + rt) \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (\$2500), - \( r \) is the rate (5% or 0.05), - \( t \) is the time in years (9). Calculating for Account I: \[ A = 2500(1 + (0.05)(9)) = 2500(1 + 0.45) = 2500 \times 1.45 = 3625 \] For Account II, the formula for compound interest is: \[ A = P(1 + r)^t \] Where: - \( P = 2500 \), - \( r = 0.08 \), - \( t = 9 \). Calculating for Account II: \[ A = 2500(1 + 0.08)^9 = 2500(1.08)^9 \] Calculating \( (1.08)^9 \approx 1.999 \): \[ A \approx 2500 \times 1.999 \approx 4997.62 \] Finally, adding both balances together: \[ \text{Total Balance} = 3625 + 4997.62 \approx 8622.62 \] Thus, the sum of the balances in Account I and Account II at the end of 9 years is approximately \( \$8622.62 \).

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