Module PF: Personal Finance
Module PF Learning Objectives:
- Convert between fractions, decimals, and percentages
- Solve for part, whole, or percent given any two of the three values
- Calculate and interpret both absolute and relative change
- Find percent increase and percent decrease
- Recognize that simple interest grows linearly
- Be able to correctly apply the simple interest formula to solve for A, r, t, or Po
- Recognize that compound interest grows exponentially
- Correctly apply the compound interest formula to solve for A, r, or Po
- Recognize that the compound interest formula is used for solving when you have a one-time, lump sum deposit
- Calculate the APY for an account earning compound interest
- Recognize that an annuity involves equal, regular payments or deposits
- Be able to correctly apply the savings annuity formula and solve for any unknown using the TVM solver
- Be able to correctly apply the payout annuity formula and solve for any unknown using the TVM solver
- Be able to correctly apply the loan formula for amortized loans and solve for any unknown using the TVM solver
- Solve real world problems that involve both planning for retirement and withdrawing from retirement accounts
- Recognize how the proportions of a payment going toward principal and interest change over the life of a loan
Section PF.1 – Percentage Basics and Applications Involving Percentages
Section PF.2 – Absolute and Relative Change
Section PF.3 – Percent Increase and Percent Decrease
Section PF.4 – Investments
Section PF.5 – Income Tax
Section PF.6 – Income Tax Decisions
Section PF.7 – Simple Interest
Section PF.8 – Compound Interest
Section PF.9 – Annual Percentage Yield (APY)
Section PF.10 – Annuities
Section PF.11 – Payout Annuities
Section PF.12 – Loans
Section PF.1 – Percentage Basics and Applications Involving Percentages
Percent literally means “per 100,” or “parts per hundred.” When we write 40%, this is equivalent to 40 per 100 which is equal to the fraction . The name of this fraction is forty-hundredths which is equivalent to the decimal 0.40.
Some fractions can be rewritten as equivalent fractions with 100 in the denominator. For example,
[latex]\frac{80}{200}[/latex] = [latex]\frac{10}{25}[/latex] = [latex]\frac{40}{100}[/latex]
- To convert a percent to a decimal, remove the % sign and divide by 100. (Or move the decimal 2 places to the left.)
- To convert a decimal to a percent, multiply by 100 then add the % sign. (Or move the decimal 2 places to the right.)
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Example 1 |
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Write each as a percent: a) [latex]\frac{1}{4}[/latex] b) 0.02 c) 2.35 d) 5/9 |
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a) [latex]\frac{1}{4}[/latex] = 25% b) 0.02 = 2% c) 2.35 = 235% d) Use your calculator 0.5556 * 100 = 55.56% |
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You Try PF.1.A |
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Complete the table below.
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| Percent |
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If we have a part that is some percent of a whole, then percent = [latex]\frac{\text{part}}{\text{whole}}[/latex] * 100 or equivalently part = [latex]\frac{\text{percent ⋅ whole}}{100}[/latex] We can convert the percent to an equivalent decimal to simplify the calculations. decimal = [latex]\frac{\text{part}}{\text{whole}}[/latex] or equivalently part = decimal ⋅ whole
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Example 2 |
| 243 people out of 400 state that they like dogs. What percent is this? |
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[latex]\frac{243}{400}[/latex] = 0.6075 Then we convert this decimal to a percent and get 60.75%.
Notice that the percent can be found from the equivalent decimal by moving the decimal point two places to the right. |
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You Try PF.1.B |
| To win the election as president of the United States of America, a person must obtain 270 out of 538 possible votes from the electoral college. What percentage of the overall electoral votes is this? Round your answer to the nearest tenth of a percent. |
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Example 3 |
| The sales tax in a town is 9.4%. How much tax will you pay on a $140.00 purchase? |
| Here, $140.00 is the whole, and we want to find 9.4% of $140.00. To do this problem, use the formula part = decimal * whole. The whole in the formula is $140.00. To compute the amount of tax: Part = 0.094(140) = $13.16 |
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You Try PF.1.C |
| In a recent poll, 28% of the 750 individuals polled indicated that they would vote purely Democratic in the next election. How many of the individuals would vote purely Democratic ballot? |
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Example 4 |
| A lender requires a minimum down payment of 12% of the value of the home. You have $22,020 cash available to use as a down payment toward a home. The down payment is the part of the house that is paid for up front when purchasing something that requires a loan. Determine the maximum home value that you can finance. |
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To compute the maximum home value, we need to understand what the $22,020.00 represents. This is the down payment; using this value we need to find the value of the home. In this case, the down payment is the “part” and the home value is the “whole.” Recall that part = decimal*whole. Let V represent the value of the home. Since we know that the down payment is 12% of the value of the home, we can write the equation: 22,020 = 0.12V. Solving this equation for V, we get V = [latex]\frac{22,020}{0.12}[/latex]= 183,500.00 So, with $22,020.00 cash available to use as a down payment, you can afford to finance a home worth at most $183,500.00. |
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You Try PF.1.D |
| One banana contains about 425mg of potassium. That is about 13% of the recommended daily amount of potassium. Using the formula part = decimal *whole, how much potassium should be consumed daily? Round your answer to the nearest whole mg. |
When working with percentages, it is very important to understand the quantities being compared. Consider the examples below.
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Example 5 |
| In the 2004 vice-presidential debates, Edwards’s claimed that US forces have suffered “90% of the coalition casualties” in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies “have taken almost 50 percent” of the casualties. Who is correct? |
| Without more information, it is hard for us to judge who is correct, but we can easily conclude that these two percentages are talking about different things, so one does not necessarily contradict the other. Edward’s claim was a percent of coalition forces, while Cheney’s claim was a percent with both coalition and Iraqi security forces. It turns out both statistics are in fact fairly accurate. |
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Example 6 |
| Over the basketball season, Isaac scores on 40% of 2-point field goal attempts, and on 30% of 3-point of field goal attempts. Find Isaac’s overall field goal percentage. |
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It is very tempting to average these values, and claim the overall average is 35%, but this is likely not correct, since most players make many more 2-point attempts than 3-point attempts. We don’t actually have enough information to answer the question. Suppose Isaac attempted 200 2-point field goals and 100 3-point field goals. For 2 point attempts, 200 is the whole. To solve this hypothetical number of points, find 40% of 200 which is 0.40(200) = 80 successful 2-point field goals For 3 point attempts, 100 is the whole. To solve this hypothetical number of points, find 30% of 100 which is 0.30(100) = 30 successful 3-point field goals. Overall, Isaac made 110 shots out of 300 field goals, for a = 36.7% overall field goal percentage. |
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Example 7 |
| What is 25% of 40? |
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To do this problem first determine what 40 represents. In this case 40 is the whole. We are trying to find the “part.” Make sure to change the percent to a decimal. part = decimal * whole part = 0.25 * 40 part = 10 The answer is 10. |
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Example 8 |
| Twenty-two is 5% of what number? |
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To do this problem it is necessary to determine if 22 is the whole or part. For this problem 22, is the part. Make sure to change the percent to a decimal. part = decimal * whole 22 = 0.05 * whole 22/0.05 = 440 The answer is 440. |
Section PF.1 – Answers to You Try Problems
PF.1.A
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[latex]\frac{3}{5}[/latex] |
0.6 |
60% |
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[latex]\frac{2}{100}[/latex] = [latex]\frac{1}{50}[/latex] |
0.02 |
2% |
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[latex]\frac{72}{100}[/latex] = [latex]\frac{18}{25}[/latex] |
0.72 |
72% |
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[latex]\frac{25}{1000}[/latex] = [latex]\frac{1}{40}[/latex] |
0.025 |
2.5% |
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[latex]4\frac{1}{2}[/latex] |
4.5 |
450% |
PF.1.B
50.2%
PF.1.C
210
PF.1.D
3,269mg
