Questions: In the past, Mike's heating bill during the winter averaged 150. This year he replaced his windows with dual-pane, energy-saving windows, and his average heating bill during the winter dropped to 90. Find percent decrease in Mike's heating bill. Julia borrowed 1200 at a high interest rate of 16%. Find the amount of interest after 1 year. 192 Jamal borrowed 2500 at an interest rate of 6%. Find the amount of interest after 2 years. 300 If Andy borrowed 1600 from a lender who charges 3.75% interest, how much interest does Andy owe after 2 years? 120 If a person borrows 2500 from a lender who charges 4.25% interest, how much interest does the person owe after 3 years? 318.75 Write each in terms of years. a) 13 months b) 39 weeks

In the past, Mike's heating bill during the winter averaged 150. This year he replaced his windows with dual-pane, energy-saving windows, and his average heating bill during the winter dropped to 90. Find percent decrease in Mike's heating bill. Julia borrowed 1200 at a high interest rate of 16%. Find the amount of interest after 1 year. 192 Jamal borrowed 2500 at an interest rate of 6%. Find the amount of interest after 2 years. 300 If Andy borrowed 1600 from a lender who charges 3.75% interest, how much interest does Andy owe after 2 years? 120 If a person borrows 2500 from a lender who charges 4.25% interest, how much interest does the person owe after 3 years? 318.75 Write each in terms of years. a) 13 months b) 39 weeks
Transcript text: In the past, Mike's heating bill during the winter averaged $\$ 150$. This year he replaced his windows with dual-pane, energy-saving windows, and his average heating bill during the winter dropped to $\$ 90$. Find percent decrease in Mike's heating bill. Julia borrowed $\$ 1200$ at a high interest rate of $16 \%$. Find the amount of interest after 1 year. $192$ Jamal borrowed $\$ 2500$ at an interest rate of $6 \%$. Find the amount of interest after 2 years. $\$ 300$ If Andy borrowed $\$ 1600$ from a lender who charges $3.75 \%$ interest, how much interest does Andy owe after 2 years? $\$ 120$ If a person borrows $\$ 2500$ from a lender who charges $4.25 \%$ interest, how much interest does the person owe after 3 years? $\$ 318.75$ Write each in terms of years. a) 13 months b) 39 weeks
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Solution

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Solution Steps

Solution Approach
  1. To find the percent decrease in Mike's heating bill, we need to calculate the difference between the old and new bills, divide by the old bill, and then multiply by 100 to get the percentage.
  2. To find the amount of interest Julia owes after 1 year, we use the formula for simple interest: \( \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \).
  3. To find the amount of interest Jamal owes after 2 years, we use the same simple interest formula.
Step 1: Percent Decrease in Heating Bill

To find the percent decrease in Mike's heating bill, we calculate the difference between the old and new bills:

\[ \text{Percent Decrease} = \frac{\text{Old Bill} - \text{New Bill}}{\text{Old Bill}} \times 100 \]

Substituting the values:

\[ \text{Percent Decrease} = \frac{150 - 90}{150} \times 100 = \frac{60}{150} \times 100 = 40.0\% \]

Step 2: Interest Owed by Julia

To find the amount of interest Julia owes after 1 year, we use the simple interest formula:

\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

Substituting the values:

\[ \text{Interest} = 1200 \times 0.16 \times 1 = 192.0 \]

Step 3: Interest Owed by Jamal

To find the amount of interest Jamal owes after 2 years, we again use the simple interest formula:

\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

Substituting the values:

\[ \text{Interest} = 2500 \times 0.06 \times 2 = 300.0 \]

Final Answer

  • Percent decrease in Mike's heating bill: \( \boxed{40.0\%} \)
  • Interest Julia owes after 1 year: \( \boxed{192.0} \)
  • Interest Jamal owes after 2 years: \( \boxed{300.0} \)
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