Beth opened a savings account and deposited $400.00 as principal. The account earns 11%
interest, compounded continuously. What is the balance after 9 years?
Use the formula A = Pe", where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (2.71828), r is the interest rate expressed as a
decimal, and t is the time in years.
Round your answer to the nearest cent.

Question

23-04-2024
Mathematics

Answered

Beth opened a savings account and deposited $400.00 as principal. The account earns 11%
interest, compounded continuously. What is the balance after 9 years?
Use the formula A = Pe", where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (2.71828), r is the interest rate expressed as a
decimal, and t is the time in years.
Round your answer to the nearest cent.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-04-23T10:42:22-04:00

Sure! To find the balance after 9 years with continuous compounding interest, we can use the formula provided: A = P * e^(rt) Given: - P (principal) = $400.00 - r (interest rate) = 11% = 0.11 (decimal) - t (time) = 9 years Now, we can substitute these values into the formula and calculate the balance after 9 years: A = 400 * e^(0.11 * 9) A = 400 * e^(0.99) A ≈ 400 * 2.69328 A ≈ 1077.312 Therefore, the balance after 9 years in the savings account, compounded continuously, would be approximately $1077.31.