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Chapter 13: Problem 67

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to solve each problem. Isabel deposits \(\$ 3000\) in an account earning \(5 \%\) per year compounded monthly. How much will be in the account after 3 yr?

Short Answer

Expert verified
Isabel will have approximately $3509.58 in her account after 3 years, given the initial deposit of $3000, an annual interest rate of 5%, and monthly compounding.

Step by step solution

01

Write down the formula

We will use the compound interest formula: \(A=P\left(1+\frac{r}{n}\right)^{n t}\), where: - A is the amount after t years, - P is the principal amount (initial deposit), - r is the annual interest rate as a decimal, - n is the number of times the interest is compounded per year, and - t is the time in years.
02

Plug in the given values into the formula

Using the given values, the formula becomes: \(A=3000\left(1+\frac{0.05}{12}\right)^{12 \cdot 3}\)
03

Calculate the amount after 3 years

Now, we will solve for A. First, find the value inside the parentheses by dividing 0.05 by 12: \(1+\frac{0.05}{12} \approx 1.0041667\) Next, raise this value to the power of 12 times 3 (which is 36): \(1.0041667^{36} \approx 1.16986\) Finally, multiply the principal amount by this value: \(A=3000 \cdot 1.16986 \approx 3509.58\) So, there will be approximately $3509.58 in the account after 3 years.

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