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题目

解题步骤

1. Understand the question

   victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?

2. Explanation

   Step1: Recall continuous compound formula

   The formula for continuous compounding is $A = Pe^{rt}$, where:

   • $P$ = principal amount,
   • $r$ = annual interest rate,
   • $t$ = time in years,
   • $A$ = final amount.

   Step2: Identify given values

   $P = 9300$, $r = 0.045$, $t = 7$

   Step3: Substitute values into formula

   $A = 9300 \times e^{(0.045 \times 7)}$

   Step4: Calculate exponent term

   First compute $0.045 \times 7 = 0.315$, so $A = 9300 \times e^{0.315}$

   Step5: Compute final amount

   $e^{0.315} \approx 1.37028$, then $A \approx 9300 \times 1.37028 = 12743.604$

3. Final answer

   $12743.60$

答案

Question Analysis

OCR Text

victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?

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