# Math homework - Part 2

MAT-120

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Chapter 8 Writing Assignment

Error analysis: Each of the following problems has an error in them. Spot the error, explain what is wrong with it, then correct it and follow through to the correct solution.

Note: The errors are marked in red.

1. If an item with an original price of $50 is on sale for 20% off, then the sale price is found by 20 x 50.

The equation for finding the sale price should be 1 minus the decimal equivalent of the sale (20% = 0.2) and then multiplied by the original price.

New Statement:

If an item with an original price of $50 is on sale for 20% off, then the sale price is found by (1 – 0.2) x 50=40.

2. If a desk is advertised at a monthly payment of $45.50 for three years, then the actual cost of this desk is $45.50 x 3 = $136.50.

Since it is a monthly payment for three years, then there are 36 payments: 12 months for each of the 3 years.

New Statement:

If a desk is advertised at a monthly payment of $45.50 for three years, then the actual cost of this desk is $45.50 x 36 = $1638

3. The amount of interest paid for a refrigerator costing $895 is found by using I = prt. So I = 895(5.8)(3) = $15,573.

Firstly, the problem itself seems to be incomplete. It is only assumed based on the equation that r=5.8 and t=3. What seems to be the mistake is that the interest meant for the refrigerator should only be 5.8% which means that it should be computed as 0.058 instead of 5.8. However it could theoretically be possible that the interest is actually 580% which is 5.8 in which case there wouldn’t be an error. However, common sense would tell us that 580% is way too large an interest rate for the refrigerator.

New Statement:

The amount of interest paid for a refrigerator costing $895 is found by using I = prt. So

I = 895(0.058)(3) = $155.73.

4. If you purchase the refrigerator mentioned in problem #3 and choose to make monthly installments for three years with an add-on interest rate of 5.8%, the monthly payment is found by $895/36 = $24.86

The total cost of the refrigerator should include the interest over the three years which we earlier computer as $155.73.

New Statement:

If you purchase the refrigerator mentioned in problem #3 and choose to make monthly installments for three years with an add-on interest rate of 5.8%, the monthly payment is found by ($895 + $155.73)/36 = $29.19.

5. If you owe $1,200 for 7 days in January and $1,000 for 24 days in February, the average daily balance for this credit card statement is [(1200 x 7) + (1000 x 24)]/30 = $1,080.

Instead of 30 days, there are 31 days to be included in the equation (7 days in Jan and 24 in Feb).

New Statement:

If you owe $1,200 for 7 days in January and $1,000 for 24 days in February, the average daily balance for this credit card statement is [(1200 x 7) + (1000 x 24)]/31 = $1,045.16

6. If $500 is deposited into an account for 4 years paying 4.5% compounded daily, then A = 500(1 + 0.045)4 = $596.26

The interest is compounded daily so that means that for 4 years, it has to be compounded 365 x 4 + 1 times (the + 1 is for the leap year which is certain every four years). Also, the rate of interest has to be divided by the number of times the amount is compounded per year which is 365.25.

New Statement:

If $500 is deposited into an account for 4 years paying 4.5% compounded daily, then A = 500[1 + 0.045/365.25](365×4+1) = $598.60