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Question 5) Jon investad \( \$ 1020 \) into a savings account for 39 weeks. He earned \( \$ 40.20 \) in intereat. A. What was the interest rate as a percent?

Ask by Ayala Horton. in Canada
Feb 26,2025

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Answer

The interest rate was approximately 5.25%.

Solution

To solve the problem, we first note that Jon’s account earned simple interest. The formula for simple interest is:   Interest = Principal × Rate × Time Here, the principal is $1020, the interest earned is $40.20, and the time is 39 weeks. Since interest rates for savings accounts are typically quoted as an annual (yearly) rate and there are 52 weeks in a year, we need to express the 39 weeks as a fraction of a year:   Time in years = 39/52 = 3/4 Plug the known values into the formula:   40.20 = 1020 × Rate × (3/4) Solve for the unknown Rate (expressed as a decimal):   Rate = 40.20 / [1020 × (3/4)]   Rate = 40.20 / (1020 × 0.75)   Rate = 40.20 / 765   Rate ≈ 0.0525 To convert the rate from a decimal to a percentage, multiply by 100:   Rate ≈ 0.0525 × 100 ≈ 5.25% So, the annual interest rate was approximately 5.25%.

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To find the interest rate as a percent, you can use the formula for simple interest: \( I = P \times r \times t \). Where \( I \) is the interest earned (\$40.20), \( P \) is the principal amount (\$1020), and \( t \) is the time in years. Since 39 weeks is approximately 0.75 years, you set up the equation: \( 40.20 = 1020 \times r \times 0.75 \). Solving for \( r \) gives you \( r = \frac{40.20}{1020 \times 0.75} \), which results in approximately \( 0.052 \). So, multiplying by 100 gives an interest rate of about \( 5.2\% \). Now, here's a fun fact: Did you know that interest rates have been around since ancient times? The Babylonians, as early as 3000 BC, had a system for lending and borrowing with interest—making it one of the world’s oldest economic concepts! If you're interested in maximizing your savings, consider diversifying your accounts! Don’t just let your money sit in one place. Research different savings accounts or even investment opportunities that might offer a higher return. Every little bit helps when it comes to growing your money!

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