Download Calculating Interest

Accounting & Finance Foundations
Math Skills
A Review
Place Value
Percentages
Calculating Interest
Discounts
Compounding
Place Value
Tenths
Hundredths
Thousands
Ten Thousands
9
1
2
3
Hundred
Thousands
Millions
Ten Thousands
Thousands
Hundreds
Tens
Ones
4
5
6
7
8
.
2
3
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
0.03
0.003
0.0003
tenths (one place to the right of decimal)
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)
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=PxRxT
Simple Interest
Examples:
• If Nadine borrows $3,500 for one year at 12% interest.
I=PxRxT
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=PxRxT
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
Finding Principal
Finding Rate
Finding Time
I = PRT
P = I/(RT)
R = I/(PT)
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 (
P = $10 / .02
P = $500
to check: $500 x 12% x 2/12 = $10
*order of operations
) first
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 (
R = 27 / 300
R = .09 or 9%
to check $900 x 9% x 4/12 = $27
*order of operations
) first
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
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
R = 15%
Finding the Time
Own Your Own
Given that: P = $1,500 I = $87.50
T = I/(PR)
*order of operations
R = 10%
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
Rate
Time
Interest
(borrowed)
1.
26,000
2.
3.
4,000
4.
500
5.
7,000
9%
48 months
6.5%
42 months
4%
160
2 years
8¾%
2730
36 months
190
Answers
Principal
Rate
Time
Interest
(borrowed)
1.
26,000
9%
48 months
$9,360.00
2.
$12,000.00
6.5%
42 months
2730
3.
4,000
4%
160
4.
500
5.
7,000
19% or
0.19
8¾%
12 months
or 1 year
2 years
36 months
$1,837.50
190
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
Rate
Time
Interest
(borrowed)
6.
300
7.
8.
1,135
9.
2,468
10.
410
15%
18 months
3%
12 months
7.15%
101.44
2 ½ years
13%
20.04
5 months
570.73
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