(Start with slide RE Math – Sect 5 – Beginning)
INTEREST MATHEMATICS
Simple Annual Interest - Real Estate loans use Simple Annual Interest. When we say SIMPLE Annual
Interest, this means we do not have to use algebra, geometry, or calculus. All we have to use is simple
addition, subtraction, multiplication, and division. If you have a hard time with these aspects of
mathematics you might need tutoring for this section.
1. Basic Interest Formula: Interest = Principal x Rate x Time
When asked how much interest will be charged the borrower should use this formula. Paid interest is a
percentage of the debt/principal owed by the borrower.
a. Interest: This is the dollar amount that a person has to pay to the lender for borrowing money.
b. Principle: This is amount of money/dollars that is borrowed. This is the amount of money owed the
lender. This amount will reduce each month with the normal monthly payments.
c. Rate: - This is the interest rate that the borrower has to pay the lender for the use of the lender's
money. To work with a percentage, we convert the percentage to a decimal. The secret is to place a
decimal in front of the percentage number.
(On the next page put slides RE Math – Sect 5 – 001 and 001A)
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Working with the Percentage Rate
Two Ways to Work with Percentage Calculations
1. Calculator Keys – When working with percentages on a calculator, you can use the “%“ key. The %
or percentage key is utilized instead of the “ = “ or equals key on most calculations.
2. Mathematically – Mathematically, the percentage is converted to a decimal that is usually less than
one. Example: Mathematically 100% = 1.00 when calculating. 22% would be calculated at .22.
When working with a percentage below 100%, we use a decimal number. We change the % to a decimal
number. Always place the decimal point 2 places to the LEFT of the percentage:
Examples: 16% = .16
10% = .10
8% = .08
5% = .05
NOTE – If you are converting a percentage to a decimal you do not use the “ % “ key on your
calculator.
(On the next page put slides RE Math – Sect 5 – 002 and 002A)
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Problem:
A $200,000 loan is subject to a 5% interest charge. How much interest is paid for the year?
Put $200,000 in your calculator and hit the ( X ) multiplication key. Now put 5 on your calculator and
hit the percentage ( % ) key. Your answer should be $10,000.
OR
Put $200,000 in your calculator and hit the ( X ) multiplication key. Now put .05 on your calculator and
hit the ( =) equals key. Your answer should be $10,000.
Problem:
A $333,000 loan is subject to a 5.8% interest charge. How much interest is paid for the year?
Put $333,000 in your calculator and hit the ( X ) multiplication key. Now put 5.8 on your calculator and
hit the percentage ( % ) key. Your answer should be $19,314.
OR
Put $333,000 in your calculator and hit the ( X ) multiplication key. Now put .058 on your calculator and
hit the ( = ) equals key. Your answer should be $19,314.
(On the next page put slides RE Math – Sect 5 – 003 and 003A)
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Working with Time
Time – Time comes into calculations regarding how long is the borrowed money subject to an interest
charge? When working with a time factor, the time should ALWAYS SHOWN IN TERMS OF YEARS.
Since there is not a time key on a calculator, we have to convert the time factor into a decimal or a
percentage.
Examples: 1 year = 1;
2 years = 2;
1 1/2 years = 1.5;
6 months = .5;
3 months = .25
Converting Months - Months are figured by make a fraction. You place the number of months over 12
since there are 12 months in a year. Then you can convert the fraction into a decimal (%) portion of a
year by dividing the top number by the bottom number.
Examples: 7 months = 7/12 of a year. Put 7 in your calculator and the division button. Now enter 12
and hit the ( = ) equals button. Your answer should be .58333% of a year.
11 month loan = 11/12 of a year. Put 11 in your calculator and hit the division button. Now enter 12 and
hit the ( = ) equals button. Your answer should be .916666% of a year.
15 month loan = 15/12 of a year. 15 divided by 12 = 1.25 years of interest charged.
NOTE: The time factor is to be multiplied ( X ) times the Percentage Charged to show the total interest
paid.
(On the next page put slides RE Math – Sect 5 – 004 and 004A)
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Interest Charged = Principal X Percentage X Time
Problem:
Helen is borrowing $20,000 for a six month period at 7% interest. How much interest will she pay?
Figure the Interest Amount First: $20,000 X 7% = $1,400.
Now the Time Factor:
6 divided by 12 = .5 of a year or 50% of a year.
$1,400 X .5 (or 50%) = $700 of interest charged.
Problem:
Bill is taking out a construction loan for his business. It is an 18 month loan of $88,000 at 8.3% interest.
What is the total interest charged?
18/12 of a year; 18 divided by 12 = 1.5 of a year or 1 ½ of a year.
$88,000 X 8.3% = $7,304 each year.
$7,304 X 1.5 of year = $10,956 of total interest charged for the 18 month loan.
(On the next page put slides RE Math – Sect 5 – 005 and 005A)
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INTEREST MATH - APPLYING THE FORMULAS
Step 1 Write the formula .. Interest = Principle X Rate X Time OR I = P x R x T.
Problem:
John borrowed $5,000 at 8% interest for 1 year. How much interest did he pay?
Answer: The interest paid (I) = $5,000 (P) x .08 (R) = $400 x 1 yr (T) = $400. John will have to pay
$400 of interest.
Problem:
If John had borrowed the money for only 6 months, how much interest would have been charged?
6/12 of year; 6 divided by 12 = .5 or 50%.
Answer: Interest Paid (I) = $5,000 (P) X .08 (R) = $400 X .5 (1/2 a Yr.) = $200 of interest.
Problem:
If John had borrowed the money for 1 year but at a 4% interest rate, how much interest would have been
charged?
Answer: Interest Paid (I) = $5,000 (P) X .04 (R) = $200 X 1 (1 year) = $200 of interest.
(On the next page put slides RE Math – Sect 5 – 006 and 006A)
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INTEREST MATH - FINDING THE "UNKNOWN"
First of all, the opposite of addition is subtraction. The opposite of multiplication is division. If we
normally multiply to get an answer, but NOW we have an unknown number, then we have to divide; the
opposite.
1. Isolate - You must also isolate the part you are looking for on one side of the equation.
2. Opposite - Crossing the equal sign means "do the opposite". If we normally multiply numbers with
one formula, we would use division to get the other number.
Example: John paid $200 in interest at 5% for a 1 year loan. How much did he borrow? Now in our
formula, the Principal(?) is the unknown.
Interest = Principal x Rate x Time is our normal formula. Now we have to find the Principal. So, we
divide (the opposite of multiplication) to get our unknown which is the Principal.
Our new formula is: Paid Interest divided by the Rate X Time = Principal.
$200 divided by .05 = $4,000 X 1 (year) = $4,000 of borrowed principal.
(On the next page put slides RE Math – Sect 5 – 007 and 007A)
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INTEREST MATH - FINDING THE "UNKNOWN"
Problem:
Bob obtained an 11% loan and paid $880 of interest each year. How much was the loan?
First of all, the $880 is charged each YEAR. So, we don’t have to figure a time factor.
Enter 880 into your calculator. Hit the division button. Now enter 11 and hit the percentage button. Your
answer should be an $8,000 loan.
OR
Enter 880 into your calculator. Hit the division button. Now enter .11 and hit the ( = ) equals key. Your
answer should be a $8,000 loan.
Problem:
Mary borrowed money for a 9 month period at 9% interest and paid $1,110 of interest. How much was
the loan amount?
9/12 of a year; Enter 9 in your calculator and hit the division button. Now enter 12 and hit the ( = )
equals button. Your Time Factor becomes .75 of a year.
Enter 1,110 in your calculator. Hit the division button. Now enter 9 and hit the percentage button. Your
answer should be $12,333.
Or
Enter 1,110 in your calculator. Hit the division button. Now enter .09 and hit the equals button. Your
answer should be $12,333.
(On the next page put slides RE Math – Sect 5 – 008) One slide only
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INTEREST MATH - FINDING THE "UNKNOWN" (continued)
Unknown is the Interest Rate.
To find the interest rate, we simply find the annual Interest charged and divide by the Principal amount
owed.
Problem 1: John borrowed $5,000 for one year and paid $350 in interest. What was the interest rate?
$350 divided by $5,000 = .07 or 7% interest.
If the time is less or greater than 1 year then we have further calculations.
Problem 2: John borrowed $18,000 for 18 months and paid $800 in interest. What interest rate did the
lender charge? John paid $800 over an 18 month period.
The unknown is the interest rate (or R). Now our formula is: Interest divided by the Principal = Rate X
Years. $800 divided by 18 months = $44.44 a month interest; 44.44 X 12 = $533.33 annual interest;
533.33 divided by $18,000 = .0296 rounded to 3%.
Problem 3: What is the interest rate if you pay $1,800 of interest a year on a $24,000 loan?
Answer: $1,800 divided by $24,000 = .075 OR 7 1/2 X 1 (yr) = 7 1/2% interest.
(On the next page put slides RE Math – Sect 5 – 009 and 009A)
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Problem:
Molly borrowed $20,000 over a 2 year period and paid a total of $3,000 in interest. What was her
interest rate?
$3,000 divided by 2 years = $1,500 a year of interest.
Put $1,500 into your calculator. Now hit the division button. Enter $20,000 and hit ( = ) equals. Your
answer should be .075 or 7.5%.
Problem:
Jim borrowed 8,000 and paid $540 over an 18 month period. What was his interest rate?
Put $540 into your computer and hit the division button. Now enter 18 and hit the ( = ) equals button.
You should get an answer of $30 per month. Put 30 in your calculator and hit the ( X ) multiplication
button. Enter 12 and hit the ( = ) equals button. Your answer should be $360 a year of Interest.
Next enter 360 and hit the division button. Now enter 8,000 and hit the ( = ) equals button. Your answer
should be .045 or 4.5%.
(On the next page put slides RE Math – Sect 5 – 010 and 010A)
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INTEREST MATH - FINDING THE "UNKNOWN" (continued)
Unknown Factor is TIME
Principal is known and the Interest Rate is known and Interest Amount is known. Now the
unknown is T (time). The formula would be P X R = I and then Actual Interest (paid) divided by Annual
Interest or Actual T (time).
Problem 1: Emily took out a 7%, $6,000 loan and paid $420 of interest. How long was the loan?
$6,000 X 7% = $420. $420 divided by $420 = 1. The loan was for 1 year.
Problem 2: Kari borrowed $10,000 at 8% and paid $1,200 of interest. How long was the loan?
$10,000 X 8% = $800 a year of interest. $1,200 divided $800 = 1.5 or 1 ½ years.
Problem 3: John borrowed $5000 at an interest rate of 6%. He paid $125 in interest. How long did he
borrow the money?
$5,000 (P) X .06 (R) = $300 Annual interest. The Actual Interest is $125; $125 divided by $300 = .4167
of year; 12 months X .4167 = 5 months.
(On the next page put slides RE Math – Sect 5 – 011 and 011A)
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Problem:
Your mother had a $4,000 9% loan and paid a total of $900 of interest. How long did she pay on this
loan?
Enter $4,000 and hit the ( X ) multiplication button. Next enter 9 and hit the percent button OR enter .09
and hit the ( = ) equals button. Your answer is $360 a year of interest.
Next put $900 on the calculator and hit the division button. Next enter 360 and hit the ( = ) equals
button. Your answer should be 2.5 years or 2 ½ years.
Problem:
Your sister took out a $5,000 8% loan and paid $100 in interest before paying off the loan. How long
was the loan in existence?
Enter $5,000 and hit the ( X ) multiplication button. Next enter 8 and hit the percentage button OR enter
.08 and hit the equals button. Your answer should be $400.
Next enter $100 and hit the division button. Enter 400 and hit the ( = ) equals button. Your answer
should be .25 or 25%. Enter 12 (months) and hit the ( x ) multiplication button. Enter 25 and hit the
percentage button OR enter .25 and hit the equals button. Your answer should be 3 or 3 months.
(On the next page put slides RE Math – Sect 5 – 012 ONLY)
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INTEREST MATH - PAYABLE INTEREST
Interest May Be Payable During the Term of the Loan.
1. Straight or Term Note: Remember, this is when we only pay interest during the term of the note.
Principal is due in one payment at the end of the loan as a balloon payment.
2. Installment or Amortized Note: Each payment is made up of some principal amount along with the
full interest owed.
3. Comparison Example: A $10,000 note at 5% interest for 5 years.
( NO SLIDE )
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REAL ESTATE NOTES - MONTHLY PAYMENTS
The vast majority of secured real estate liens require monthly amortized payments. For this reason, any
State examination that you might take will be based on this basis as well.
Example 1: John has a $20,000 amortized loan at 10% interest for a loan term of 35 years. His monthly
payments are $171.94 per month of principal and interest. How much does he owe at the end of the 1st
payment?
a. I = P x R x T; I = $20,000 x .10 x .08333 (1/12) = $166.67 of interest per month.
1) I = $166.67; so, $171.94 payment - $166.67 of interest = $5.27 toward principal.
2) $20,000 - $5.27 = $19,994.73 would be owed after 1 month. PITI.
Example 2: John has a $40,000 loan at 7.5% interest for 30 years. His monthly payments are $349.70
and include reserves for taxes and insurance. The annual tax is $660 a year and the insurance policy
costs $180 a year. What does John owe at the end of the 1st payment?
a. Reserves are deducted first. This is $660 + $180 = $840 per year.
1) $840.12 divided by 12 months = $70 per month goes to reserves first.
2) $349.70 - $70 for reserves = $279.70 left for principal and interest.
b. I = P x R x T; I = $40,000 x .075 x .08333; I = $250.00 for the month.
1) $279.70 - $250.00 interest = $29.70 principal.
2) $40,000 - $29.70 = $39,970.30 remaining.
(On the next page put slides RE Math – Sect 5 – 014 and 014A)
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Problem:
Harry has a property tax requirement of $2,000 a year. His Fire Insurance is $400 a year. If he has a
monthly payment of $1,400 on his 30 year $200,000 loan at 6%, what is the interest amount the first
month?
Do the Problem:
We do not need the property tax or insurance figures for this question. We only have to calculate the
interest the first month.
Enter 200,000 in your calculator and hit the ( X ) multiplication key. Enter 6 and hit the ( % ) percentage
key OR enter .06 and hit the ( = ) equal key. Your answer should be $12,000. Now hit the division key
and enter 12 and hit the ( = ) equals key. Your answer should be $1,000 of interest the first month.
How much of principal was reduced after the first month?
Do the Problem:
The property tax and insurance is $2,400 a year. Enter 2,400 and hit the division button. Now put 12 into
your computer and hit the ( = ) equals button. The answer should be $200 per month.
Enter the monthly payment of $1,400 and hit the minus ( - ) button. Now enter $200. Hit the ( - ) button
again and enter $1,000. Now hit the ( = ) equals button. Your answer should be $200. Now enter
$200,000 and hit the ( - ) minus button. Lastly, enter $200 and hit the equals button. Your answer should
be $199,800 of owed principal after the first monthly payment.
(On the next page put slides RE Math – Sect 5 – 015 and 015A)
(On the next page put an ENDING SLIDE)
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