QuestionDecember 17, 2025

18 Jackson deposited 5,000 3.8% interest, compounded controusesly, when he was 18 years old.How much will be in the account when he is 40 years old if he made no other deposits or Jackson deposited 5,000 withdrawals? (10A2.b,3.9) A 8,800.00 B 11,535.60 C 19,000.19 D 10,691.38

18 Jackson deposited 5,000 3.8% interest, compounded controusesly, when he was 18 years old.How much will be in the account when he is 40 years old if he made no other deposits or Jackson deposited 5,000 withdrawals? (10A2.b,3.9) A 8,800.00 B 11,535.60 C 19,000.19 D 10,691.38
18 Jackson deposited 5,000 3.8% interest, compounded controusesly, when he was 18 years old.How much will be in the account when he is 40 years old if he made no other deposits or Jackson deposited 5,000 withdrawals? (10A2.b,3.9) A 8,800.00 B 11,535.60 C 19,000.19 D 10,691.38

Solution
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Answer

\11,535.60 Explanation 1. Identify the formula for continuous compounding Use A = Pe^{rt}, where P is principal, r is rate, t is time. 2. Substitute values P = 5000, r = 0.038, t = 40 - 18 = 22 years. 3. Calculate exponent rt = 0.038 \times 22 = 0.836 4. Compute e^{0.836} e^{0.836} \approx 2.307 5. Find final amount A = 5000 \times 2.307 = 11,535

Explanation

1. Identify the formula for continuous compounding<br /> Use $A = Pe^{rt}$, where $P$ is principal, $r$ is rate, $t$ is time.<br />2. Substitute values<br /> $P = 5000$, $r = 0.038$, $t = 40 - 18 = 22$ years.<br />3. Calculate exponent<br /> $rt = 0.038 \times 22 = 0.836$<br />4. Compute $e^{0.836}$<br /> $e^{0.836} \approx 2.307$<br />5. Find final amount<br /> $A = 5000 \times 2.307 = 11,535$
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