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On July 7, Joelle had a savings account with a beginning principal of $2700. It earned 4.5% interest, compounded daily. On July 8, she deposited her first paycheck of $476.52 and she withdrew $1250. What was her balance at the end of the day on July 8th?

User Fahim
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Answer: $1926.52.

Explanation: To calculate Joelle's balance at the end of the day on July 8th, we need to consider the initial principal, the interest earned, the paycheck deposit, and the withdrawal.

First, let's calculate the interest earned on the initial principal of $2700. The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the time the money is invested or borrowed for, in years

In this case, the interest is compounded daily, so n = 365.

Using the formula, we can calculate the interest earned on the initial principal:

A = 2700(1 + 0.045/365)^(365*1)

A ≈ 2700(1 + 0.0001238)^365

A ≈ 2700(1.0001238)^365

A ≈ 2700(1.045)

The interest earned is approximately $283.50.

Next, let's calculate Joelle's balance after depositing her paycheck:

Balance after deposit = Initial balance + Paycheck deposit

Balance after deposit = 2700 + 476.52

Balance after deposit = 3176.52

Lastly, let's calculate Joelle's balance after the withdrawal:

Balance after withdrawal = Balance after deposit - Withdrawal amount

Balance after withdrawal = 3176.52 - 1250

Balance after withdrawal = 1926.52

Therefore, Joelle's balance at the end of the day on July 8th is $1926.52.

User Jonathan Mayer
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