Mathematics Answer Note #13

Question 1 Assuming you invest $1000 at an annual interest rate of 5%, compounded annually, how much will your investment have grown after 5 years? Answer Based on the given information, we can use the compound interest formula A = P*(1+r)^n to calculate the growth of the investment after 5 years. In this formula, A represents the final amount, P represents the principal amount invested, r represents the annual interest rate, and n represents the number of compounding periods. First, we need to determine the annual interest rate, which is 5% or 0.05 in decimal form. Next, we need to determine the number of compounding periods, which is 5 years or 5 periods. Then, we can plug these values into the formula: A = $1000*(1+0.05)^5 = $1000*(1.05)^5 = $1000*1.2762815625 = $1276.28 Therefore, after 5 years, the investment will have grown to $1276.28. We can also break down the growth for each year to better understand the impact of compounding interest: Year 1: $1000*(1+0.05)^1 = $1000*1.05 = $1050 Year 2: $1050*(1+0.05)^1 = $1050*1.05 = $1102.50 Year 3: $1102.50*(1+0.05)^1 = $1102.50*1.05 = $1157.62 Year 4: $1157.62*(1+0.05)^1 = $1157.62*1.05 = $1215.50 Year 5: $1215.50*(1+0.05)^1 = $1215.50*1.05 = $1276.28 Question 2 Lucy is working at an elementary school after-care program to get experience teaching before she goes to college. Since she is still in school, she can only work 12 to 15 hours per week. Her pay rate is $12.50 an hour, and unless she works the max of 15 hours a week, then the last hour is paid out at $14. Which of the following is a possible amount for her check on any given week? Assume she can only work for a full hour, i.e., she cannot get paid $6.25 for working a half hour. A. $162.50 B. $168 C. $176.50 D. $210 Answer Based on the given information, the correct answer is C. $176.50. This is because if Lucy works the maximum of 15 hours a week, she would earn $187.50 (15 hours at $12.50 per hour) plus $14 for the last hour, bringing her total earnings to $201.50. However, since she can only work for a maximum of 15 hours, she cannot earn the full $187.50 and therefore her check amount would be $176.50. This can also be calculated by multiplying the hours worked (12) by the pay rate of $12.50 per hour and adding the extra $14, resulting in $176.50. Question 3 Claro, aquí tienes la traducción al inglés del ejercicio: Ana and Juan have a collection of books. If Ana gives 15 of her books to Juan, they will both have the same number of books. However, if Juan gives 10 of his books to Ana, she will have twice as many books as Juan. How many books does each one have originally? Answer After carefully analyzing the given information, we can determine that this is a problem involving two variables, Ana and Juan, and the number of books each of them originally has in their collection. In order to solve this problem, we will use algebraic equations and reasoning. Let us assign the variables "a" and "j" to represent the number of books that Ana and Juan have, respectively, in their collections. From the given information, we can set up the following equations: 1. Equating the number of books after Ana gives 15 of hers to Juan: a - 15 = j + 15 2. Equating the number of books after Juan gives 10 of his to Ana: a + 10 = 2(j - 10) To make the problem simpler, let us solve equation 1 for "a": a = j + 30 Now, we can substitute this value of "a" into equation 2: j + 30 + 10 = 2(j - 10) Simplifying this equation, we get: j + 40 = 2j - 20 Rearranging the terms, we get: j = 60 Substituting this value of "j" into our equation for "a": a = 60 + 30 = 90 Therefore, Ana originally had 90 books in her collection, and Juan originally had 60 books in his collection. Question 4 Daniel's checking account balance is $398.35. He writes a check for $125.00 to donate to his favorite public radio station. Then, he withdraws $80.00 in cash to buy tickets to a concert. How much money remains in Daniel's account? Answer After calculating the transactions that Daniel made, we can determine the remaining balance in his checking account. Firstly, let's subtract the amount he donated to the public radio station which is $125.00 from his initial balance of $398.35. This leaves Daniel with $398.35 - $125.00 = $273.35 in his account. Next, we need to subtract the amount he withdrew to buy concert tickets, which is $80.00. Therefore, the amount remaining in Daniel's account is $273.35 - $80.00 = $193.35. Question 5 Nolan has $1.80 in his pocket. His mom gives him $3.50. He goes to the store and spends $4.29 on chips, an apple, and a candy bar. How much money does he have left? Answer Based on the information given, Nolan initially had $1.80 and received an additional $3.50 from his mom, giving him a total of $5.30. After spending $4.29 on chips, an apple, and a candy bar, Nolan is left with $1.01.