Accounting & Finance Foundations Math Skills A Review. Place Value Percentages Calculating Interest Discounts Compounding

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1 Accounting & Finance Foundations Math Skills A Review Place Value Percentages Calculating Interest Discounts Compounding

2 Place Value Ten Thousands Thousands Hundredths Tenths Ones Tens Hundreds Thousands Ten Thousands Hundred Thousands Millions

3 Converting Percentages and Decimals Notes

4 Why Important? 2% = % = $100 x 0.02 = $2 $100 x 0.20 = $20 an $18 difference

5 Percentages to Decimal To convert a percentage to a decimal, move the decimal two places to the left. Example: 8.6% = % = 0.50

6 Converting Percentages to a Decimal Practice 12% =? 9.5% =? 100 % =?

7 Converting Percentage to Decimal Answers Move decimal two places to the left and drop the % sign. 12% = % = % = 1.0

8 Converting Decimal to Percentage To convert a decimal to a percentage move the decimal two places to the right and add a percentage sign. Example: 0.50 = 50% 1.25 = 125% 0.04 = 4%

9 Converting Decimal to Percentage Practice 0.06 = 0.84 = = 1.00 =

10 Converting Decimal to Percentage Answers Move the decimal two places to the right and add a percentage sign = 6% 0.84 = 84% =0.2% 1.00 = 100%

11 Rounding Notes

12 Rounding 0.3 tenths (one place to the right of decimal) 0.03 hundredths (two places to the right of the decimal) thousandths (three places to the right of the decimal) ten thousandths (four places to the right of the decimal)

13 Rounding Look at the first number to the right of the place rounding to. If 5 or above round up one number If below a 5 leave the number as is Drop all numbers to the right of the named place value. Example: Round to tenths place (one place to the right of decimal) = 0.2 (look at the first number to the right of the tenths place the 3, it is below a 5 so no rounding) = 0.4 (look at the 5 it is a 5 or higher so round up)

14 Rounding rounded to the tenth place (one place to the right of the decimal) Answer = 25.2 (drop all numbers to the right of the tenth place) rounded to the hundredth (two places to the right of the decimal) Answer = (drop all numbers to the right of the hundredth place)

15 Rounding Practice Round to the hundredths place (two places to the right of the decimal) = = = =

16 Rounding Answers Round to the hundredths place (two places to the right of the decimal) = 1.22 (3 is below a 5 so just drop the 3 and 4) = (8 is above a 5 so round up one, drop remaining numbers) = = 0.01

17 Calculating Simple Interest Notes

18 Calculating Simple Interest for Loans Simple Interest (Ordinary Interest) is used when a loan is paid in one lump sum at the end of the loan period. I = interest (amount paid for using the loaned money) P = principal (amount borrowed) T = time (length of time of the loan) R = rate (percentage of interest charged per year) The formula is I = P x R x T

19 Simple Interest Examples: If Nadine borrows $3,500 for one year at 12% interest. I = P x R x T I = $3,500 x 12% x 1 = $ $420 + $3,500 = $3,920 (amount to be repaid at the end of the loan) practical math app pg 279

20 Simple Interest If the loan was only for 8 months, then: I = $3,500 x 12% x 8/12 OR I = $3,500 x 12% x 8 12 = $ $280 + $3,500 = $3,780 (amount to be repaid at the end of the loan) [here, treat the time (T) as a percentage] practical math app pg 279

21 Practice Own-Your-Own Calculate simple interest for the following: 1. $3,000 at 9% for 2 years 2. $1,450 at 15% for 8 months 3. $800 at 13% for 3 months 4. $1,680 at 12% for 6 months 5. $600 at 16% for 5 months

22 Answers 1. $3,000 at 9% for 2 years $3,000 x.09 x 2 = $ $1,450 at 15% for 8 months $1,450 x.15 x 8/12 = $ $800 at 13% for 3 months $800 x.13 x 3/12 = $26

23 Answers cont 4. $1,680 at 12% for 6 months $1,680 x.12 x 6/12 = $ $600 at 16% for 5 months $600 x.16 x 5/12 = $40

24 Exact Interest & Number of Days Calculating Exact Interest Based on Number of Days Assume 365 days in a year. (sometimes 360 days is used) I = P x R x T Loan of $4,000 at 9% for 60 days. I = $4,000 x.09 x 60/365 OR I = $4,000 x.09 x = $59.18 practical math app pg 281

25 Exact Interest & Number of Days Calculate the following: $2,000 at 12% for 60 days $10,500 at 13% for 30 days $1,250 at 8% for 45 days practical math app pg 281

26 Exact Interest Based on 365 Days Answers $2,000 at 12% for 60 days $2,000 x 0.12 x 60/365 = $2,000 x 0.12 x = $39.45 Therefore, for a 60 day loan with these terms you would pay $39.45 to use the $2,000

27 Exact Interest Based on 365 Days Answers $10,500 at 13% for 30 days $10,500 x 0.13 x 30/365 = $10,500 x 0.13 x = $ Therefore, for a 30 day loan with these terms you would pay $ to use the $10,500

28 Exact Interest Based on 365 Days Answers $1,250 at 8% for 45 days $1,250 x 0.08 x 45/365 = $ Rounded to $12.33

29 Formulas Simple (Ordinary) Interest Finding Principal Finding Rate Finding Time I = PRT P = I/(RT) R = I/(PT) T = I/(PR)

30 Finding the Principal Given that: R = 12% I = $10 T = 2 months P = I/(RT) P = $10 / (.12 x 2/12) *do calculation in ( ) first P = $10 /.02 P = $500 to check: $500 x 12% x 2/12 = $10 *order of operations

31 Finding the Principal On Your Own Given that: R = 11% I = $12 T = 3 months P = I/(RT) *do calculation in ( ) first

32 Finding the Principal Own Your Own Answer P = I/(RT) Given that: R = 11% I = $12 T = 3 months P = 12 / (.11 x 3/12) P = 12 /.0275 P = = $ To check $ x 11% x 3/12 = $ interest

33 Finding the Rate Given that: P = $900 I = $27 T = 4 months R = I/(PT) R = 27 / (900 x 4/12) *do calculation in ( ) first R = 27 / 300 R =.09 or 9% to check $900 x 9% x 4/12 = $27 *order of operations

34 Finding the Rate Own Your Own Given that: P = $800 I = $8.00 T = 2 months R = I/(PT) *order of operations

35 Finding the Rate Own Your Own Answer R = I/(PT) Given that: P = $800 I = $8.00 T = 2 months R = 8 / (800 x 2/12) R = 8 / R = = 6% To check $800 x 6% x 2/12 = $8.00

36 Finding the Time Given that: P = $1,200 I = $45 R = 15% T = I/(PR) T = 45 / ($1,200 x.15) T = 45 / $ T =.25 or 25/100 = ¼ = 3 months to check: $1,200 x.15 x 3/12 = $45 *order of operations

37 Finding the Time Own Your Own Given that: P = $1,500 I = $87.50 R = 10% T = I/(PR) *order of operations

38 Finding the Time T = I/(PR) Own Your Own Answer Given that: P = $1,500 I = $87.50 R = 10% T = / 1500 x.10 T = / 150 T = or 12 mths x = mths or 7 mths To check $1,500 x 10% x 7/12 = $87.50

39 For a Grade Principal Rate Time Interest (borrowed) 1. 26,000 9% 48 months % 42 months ,000 4% years ,000 8 ¾ % 36 months

40 Answers Principal (borrowed) Rate Time Interest 1. 26,000 9% 48 months $9, $12, % 42 months ,000 4% 12 months or 1 year % or years ,000 8 ¾ % 36 months $1,837.50

41 Answers 1. $26,000 x 0.09 x 48 / 12 = $9, $2,730 / (0.065 x 42 / 12) = $2,730 / = $12, $160 / ($4,000 x 0.4) = $160 / 160 = 1 year 4. $190 / ($500 x 2) = $190 / 1,000 = 0.19

42 For a Grade Principal Rate Time Interest (borrowed) % 18 months 7. 3% 12 months , % ,468 2 ½ years % 5 months

43 Discounts Some companies often give businesses discounts for paying early. Example: terms are 1/10, n/30 1 % discount if paid in 10 days Net amount due in 30 days If invoice is for $500, then could save $5 by paying early. Why does the company do this?

44 Discounts $300 invoice dated August 1, terms are 2/15, n/30. How much is owed if paid on August 13?

45 Discounts answer $300 invoice dated August 1, terms are 2/15, n/30. How much is owed if paid on August 13? $300 x 2% = $6 $300 - $6 discount = $294

46 Compound Interest Compounding occurs when your investment earnings or savings account interest is added to your principal, forming a larger base on which future earnings may accumulate. As your investment base gets larger, it has the potential to grow faster. And the longer your money is invested, the more you stand to gain from compounding. For example, say you earn 5% compound interest on $100 every year for five years. You'll have $105 after one year, $ after two years, $ after three years, and $ after five years.

47 Compound Interest Without compounding, you earn simple interest, and your investment doesn't grow as quickly. For example, if you earned 5% simple interest on $100 for five years, you would have $125. A larger base or a higher rate provide even more pronounced differences. Compounding can occur annually, monthly, or daily. Example: $200 earning 5%, compounded monthly for one year 1 st month $200 x 5% x 1/12 = = $ nd month $ x 5% x 1/12 = = $ rd month $ x 5% x 1/12 = = $202.51