Accounting & Finance Foundations Math Skills A Review ... Interest... · Place Value...

Place Value

Percentages

Calculating Interest

Discounts

Compounding

Accounting & Finance Foundations

Math Skills

A Review

Place Value

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Converting Percentages

and Decimals

Notes

Why Important?

• 2% = 0.02

• 20% = 0.20

• 0.02 ≠ 0.20

• $100 x 0.02 = $2

an $18 difference

• $100 x 0.20 = $20

Percentages to Decimal To convert a percentage to a decimal, move the decimal two places to the left.

Example:

8.6% = 0.086

50% = 0.50

Converting Percentages to a Decimal

Practice

• 12% = ?

• 9.5% = ?

• 100 % = ?

Converting Percentage to Decimal Answers

• Move decimal two places to the left and

drop the % sign.

• 12% = 0.12

• 9.5% = 0.095

• 100% = 1.0

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%

Converting Decimal to Percentage

Practice

• 0.06 =

• 0.84 =

• 0.002 =

• 1.00 =

Converting Decimal to Percentage

Answers

• Move the decimal two places to the right

and add a percentage sign.

• 0.06 = 6%

• 0.84 = 84%

• 0.002 =0.2%

• 1.00 = 100%

Rounding

Notes

Rounding

0.3 tenths (one place to the right of decimal)

0.03 hundredths (two places to the right of the decimal)

0.003 thousandths (three places to the right of the decimal)

0.0003 ten thousandths (four places to the right of the decimal)

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)

• 0.2344 = 0.2 (look at the first number to the right of the tenths

place—the 3, it is below a 5 so no rounding)

• 0.3544 = 0.4 (look at the 5—it is a 5 or higher so round up)

Rounding

25.234 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)

25.369 rounded to the hundredth (two places to

the right of the decimal)

Answer = 25.37 (drop all numbers to the right of the hundredth

place)

Rounding Practice

• Round to the hundredths place (two places

to the right of the decimal)

• 1.2234 =

• 20.3587 =

• 0.0143 =

• 0.0056 =

Rounding Answers

• Round to the hundredths place (two places

to the right of the decimal)

• 1.2234 = 1.22 (3 is below a 5 so just drop the 3 and 4)

• 20.3587 = 20.36 (8 is above a 5 so round up one, drop

remaining numbers)

• 0.0143 = 0.01

• 0.0056 = 0.01

Calculating Simple Interest

Notes

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

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 = $420.00

$420 + $3,500 = $3,920 (amount to be repaid at the end of the loan)

practical math app pg 279

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 = $280.00

$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

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

Answers

1. $3,000 at 9% for 2 years

$3,000 x .09 x 2 = $540

2. $1,450 at 15% for 8 months

$1,450 x .15 x 8/12 = $145

3. $800 at 13% for 3 months

$800 x .13 x 3/12 = $26

Answers cont…

4. $1,680 at 12% for 6 months

$1,680 x .12 x 6/12 = $100.80

5. $600 at 16% for 5 months

$600 x .16 x 5/12 = $40

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 60 ÷ 365 = $59.18 practical math app pg 281

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

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 60 ÷ 365 = $39.45

Therefore, for a 60 day loan with these terms you would pay $39.45 to use the $2,000

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 30 ÷ 365 = $112.19

Therefore, for a 30 day loan with these terms you

would pay $112.19 to use the $10,500

Exact Interest Based on 365 Days

Answers

$1,250 at 8% for 45 days

$1,250 x 0.08 x 45/365 = $12.3287

Rounded to $12.33

Formulas

• Simple (Ordinary) Interest I = PRT

• Finding Principal P = I/(RT)

• Finding Rate R = I/(PT)

• Finding Time T = I/(PR)

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

Finding the Principal

On Your Own

Given that: R = 11% I = $12 T = 3 months

P = I/(RT)

*do calculation in ( ) first

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 = 436.36363 = $436.36

To check $436.36 x 11% x 3/12 = $11.9999 interest

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

Finding the Rate

Own Your Own

Given that: P = $800 I = $8.00 T = 2 months

R = I/(PT)

*order of operations

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 / 133.33

R = 0.06000015 = 6%

To check $800 x 6% x 2/12 = $8.00

Finding the Time

Given that: P = $1,200 I = $45 R = 15%

T = I/(PR)

• T = 45 / ($1,200 x .15)

• T = 45 / $180.00

• T = .25 or 25/100 = ¼ = 3 months

• to check: $1,200 x .15 x 3/12 = $45

*order of operations

Finding the Time

Own Your Own

Given that: P = $1,500 I = $87.50 R = 10%

T = I/(PR)

*order of operations

Finding the Time

Own Your Own Answer

T = I/(PR)

Given that: P = $1,500 I = $87.50 R = 10%

T = 87.50 / 1500 x .10

T = 87.50 / 150

T = 0.5833333 or 12 mths x 0.583 = 6.996 mths or 7 mths

To check $1,500 x 10% x 7/12 = $87.50

For a Grade

Principal (borrowed)

Rate Time Interest

1. 26,000 9% 48 months

2. 6.5% 42 months 2730

3. 4,000 4% 160

4. 500 2 years 190

5. 7,000 8 ¾ % 36 months

Answers

Principal (borrowed)

Rate Time Interest

1. 26,000 9% 48 months $9,360.00

2. $12,000.00 6.5% 42 months 2730

3. 4,000 4% 12 months

or 1 year

160

4. 500 19% or

0.19

2 years 190

5. 7,000 8 ¾ % 36 months $1,837.50

Answers 1. $26,000 x 0.09 x 48 / 12 = $9,360.00

2. $2,730 / (0.065 x 42 / 12) =

$2,730 / 0.2275 = $12,000

3. $160 / ($4,000 x 0.4) =

$160 / 160 = 1 year

4. $190 / ($500 x 2) =

$190 / 1,000 = 0.19

For a Grade

Principal (borrowed)

Rate Time Interest

6. 300 15% 18 months

7. 3% 12 months 20.04

8. 1,135 7.15% 101.44

9. 2,468 2 ½ years 570.73

10. 410 13% 5 months

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?

Discounts

• $300 invoice dated August 1, terms are

2/15, n/30. How much is owed if paid on

August 13?

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

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, $110.25 after two years, $115.76 after three

years, and $127.63 after five years.

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

• 1st month $200 x 5% x 1/12 = .83 + 200 = $200.83

• 2nd month $200.83 x 5% x 1/12 = .84 + 200.83 = $201.67

• 3rd month $201.67 x 5% x 1/12 = .84 + 201.67 = $202.51