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Chapter 20: MATH & REAL ESTATE
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Terms in this set (79)
The VARIABLES in Profit or Loss problems are as follows:
Example Question
Owner bought his home for $30,000 and later sold it for $33,000.
What percent of profit did he make?
A property was bought for $45,000 and sold at a 20% profit. What was the selling price?
A building was sold for $23,000 at a profit of 15%.
What was the original purchase price?
If the EARNINGS is greater than the PRINCIPAL, the RATE is greater than 100%.
...
WHEN PROPERTY IS SOLD AT A LOSS, the RATE will be less than 100%
...
Owner bought a home for $20,000 and sold it at a 5% loss. What was the selling price?
Interest
Interest is a charge which you pay a lender when you borrow money. It is rent which is paid for the use of someone else's money.
Interest Math Problem Variables
TYPES OF INTEREST
1. Simple Interest: Paid only on the unpaid balance owing.
2. Compound Interest: Paid on the balance plus the accrued interest.
3. Add-On Interest: The interest is determined for the life of the loan, and then added to the principal. The borrower signs a note for the principal and interest combined and pays it back in equal monthly installments. (This is commonly used for installment sales and results in almost double interest, since the borrower is paying for the use of money which he already paid back.)
4. Discount Interest: Borrower signs a note for the principal and interest combined, but only receives the principal. He then pays interest on the full amount of the note.
Note: In this section we will be dealing with simple interest only.
What is the interest on a loan of $20,000 at 8% for one year?
What is the interest on a loan of $20,000 at 8% for one year?
What is the interest on a loan of $20,000 at 8% for one year?
In the above example, what would be the interest for 2 years and 6 months?
RULES IN CALCULATING INTEREST
1. Interest may be calculated annually, semi-annually (1/2 of annual), quarterly (1/4 of annual), monthly (1/12 of annual) or daily (1/360 of annual).
2. In calculating interest on a daily basis, we use a 360 day year with each month having 30 days regardless of the month.
On a loan of $6,000 at 6%, what is the interest due for 3 months and 5 days?
INTEREST ON REAL ESTATE LOANS may be figured in one of two ways.
Level Principal Payment.
Direct Reduction Loan.
Level Principal Payment.
An equal amount on principal is paid each month plus interest which diminishes as the principal goes down.
Direct Reduction Loan.
he total monthly payment, which includes principal and interest, remains the same during the life of the mortgage. The interest portion of the payment decreases as the principal payments increase. Special mortgage loan payment charts are used to determine the monthly payments and the monthly amortization of the principal.
What is the interest due for the first and second months on a mortgage of $12,000 for 20 years with 6% interest per annum if the principal is paid in equal monthly installments?
Principal payment = $12,000 ÷ 240 (months) = $50/month
Annual interest on $12,000 @ 6% = .06 x $12,000 = $720.
Interest for one month = $720 ÷ 12 = $60.
First month's interest = $60
Principal, after first month's payment has been reduced to $11,950.
Annual interest on $11,950 = .06 x $11,950 = $717.
Interest for one month = $717 ÷ 12 = $59.75
First month's interest is $60. Second month's interest in $59.75.
Brown has a $40,000 mortgage on his home. The interest rate is 12% per annum. The monthly mortgage payment on P.&I. is $421.29.
What is the balance due on the mortgage after the first payment?
DISCOUNTS ‒ POINTS, ORIGINATION FEES
Mortgage lenders often charge discounts to increase their "effective yield" when making loans at competitive interest rates or attractive repayment terms.
The discount is a charge made at the inception of the loan and is measured in points, with each point representing a charge of 1% of the loan.
Federal regulations allow either party in the sale to pay discount points on conventional and F.H.A. mortgages.
Discount points may not be charged to buyers in V.A. loan transactions.
Bank approves a mortgage for $60,000 for a customer. The bank will write the mortgage at a fixed rate of interest of 13% per year, or at a variable interest rate of 11% for the first year. The bank requires 4 points for the variable rate mortgage.
How much is the discount charge to be paid at the closing?
Solution: .04 x $60,000 = $2,400.
Service Charge or Origination Fee.
his is a one time charge also measured in points made by the bank when originating a loan. It is usually paid by the buyer and in the case of a V.A. loan the buyer may pay no more than 1%.
Sale price is $90,000 and the bank agrees to loan 80% of the value of the property. If the bank charges 3 points, what will be the discount charge to close the loan?
Solution: .80 x $90,000 = $72,000 x .03 = $2,160
CAPITALIZATION
An apartment building has an annual net income of $18,000. If the capitalization rate for this type of property is 9%, what is the estimate of value?
What is the expected net annual income on a property valued at $180,000 with a capitalization rate of 12%?
A building valued at $80,000 produced an annual net income of $6,400. What is its capitalization rate?
NET ANNUAL INCOME
is arrived at after deducting normal operating expenses. Principal and interest payments on a mortgage are not considered as an expense. The capitalization rate for the property is determined by an appraiser and reflects what an investor would expect as a rate of return for a particular type of property.
RATE OF RETURN ON INVESTMENT
is the actual rate of return produced by an investment based upon its annual net income.
[RATE OF RETURN = CAPITALIZATION RATE]
Rate of Return is actually the same as Capitalization rate and the terms are used interchangeably
An apartment building valued at $90,000, to earn 15% on the total investment annually, should return a net monthly income in what amount?
Owner's building produced a semi-annual gross income of $8,000. His expenses were 60% of his gross income. If the capitalization rate is 8%, what is the building worth?
RATE OF RETURN ON CASH INVESTED
When using capitalization rate, the property is treated as being free and clear with no mortgage. The return on investment is not the actual cash received in hand, since the mortgage payments are not taken into consideration. Most investors want to know what they can expect as a return on their cash invested after deducting all expenses including debt service (mortgage payments).
An investor buys a building for $120,000 and puts down $30,000 in cash. If net income is $9,600 and mortgage payments are $6,000 annually, what is his rate of return on cash invested?
GROSS INCOME MULTIPLIER (GIM).
This is a method of evaluating income property by multiplying the gross annual income by a number or factor determined from comparable properties. The GIM is not a reliable or acceptable approach in appraising.
Income properties in the area are selling for 8 times the gross annual income. If you are considering buying a comparable building with a gross annual income of $30,000, how much would you pay for the building?
GROSS RENT MULTIPLIER (GRM)
is a yardstick used in evaluating one-family residences or duplexes which are owned for rental income. Value is determined by multiplying the monthly rent by a number or factor developed from comparable sales. For example, a single family home with a monthly rent of $400 sells for $60,000 or 150 times the monthly gross rent. If you were considering buying a comparable property with a $500 monthly rent, applying the GRM, it would be worth $75,000.
DEPRECIATION
STRAIGHT LINE DEPRECIATION
The value of the improvement depreciated by an equal amount or percentage each year during its estimated economic life. Straight line depreciation will be used exclusively in these problems.
Ex: a) A building worth $100,000 depreciates at a rate of 2% per year. Its annual amount of depreciation is $2,000 per year.
is determined by dividing the economic life (in years) into 100%.
Example: A building with an economic life of 50 years will have a depreciation rate of 2%. (100% ÷ 50 = 2%)
DEPRECIATION RATE is determined by
is determined by dividing the economic life (in years) into 100%.
Example: A building with an economic life of 50 years will have a depreciation rate of 2%. (100% ÷ 50 = 2%)
To determine annual depreciation, the variables are as follows:
A building which cost $180,000 to construct depreciates at 4% annually. What is the yearly depreciation in dollars?
To determine total amount of depreciation, the variables are:
A building cost $80,000 to reproduce. It is now 8 years old and has depreciated at a rate of 5% annually.
How much has it depreciated to date?
To determine present value (market value, or remaining value), use the formula as follows:
A building cost $80,000 new. It is now 6 years old and has depreciated at a rate of 4% annually.
What is its current value?
REAL ESTATE TAX PROBLEMS
Real estate taxes are charges levied against real estate according to its value in order to help pay for the municipality's budget. The amount of the tax is determined by multiplying the assessed value by the tax rate.
TAX RATE
A rate established by a municipality by dividing the total assessed valuation into the annual budget.
Ex: Bigtown has an annual budget of $336,000 and the total assessed value of the property is $8,000,000. What is the tax rate?
MILLS
ASSESSED VALUATION.
This is the value established by a city or town for tax purposes. It is usually based upon a percentage of market value.
APPLYING THE FORMULA FOR SOLVING TAX PROBLEMS
a) A property is assessed at 60% of market value of $40,000. What is the tax if the rate is $42 per thousand?
The taxes on a home are $600. If the tax rate is $30 per thousand and the property is assessed at 50% of market value, what is the market value?
Market value is $60,000. Property is assessed at 80% of market value. Taxes for the year are $1,536. What is the tax rate?
DEED TAX STAMPS OR TRANSFER TAX
Most states require a deed tax or transfer tax. The amount and who pays the tax varies according to state law. There is no federal deed tax. Some states tax only the equity (price less take-over encumbrances) while others tax the full purchase price. Check the law of your state.
PRORATING
Proration Rules:
1) Prorations are made to, and including, day of closing. Seller is usually responsible for the day of closing.
2) Calculate time involved. (Either seller's time or buyer's time depending whether item is owed or prepaid.
3) In prorating, a year has 360 days, there are 12 months to a year and each month has 30 days regardless of the month.
4) Carry your figures three places to the right of the decimal point until your final answer, then round off to 2 decimal places. Round up 1¢ if the third decimal is five or larger.
5) To determine who owes what, ask the following questions?
a) HAS THE EXPENSE BEEN PAID?
b) WHO PAID THE EXPENSE?
c) WHO HAS, OR WILL, RECEIVE THE BENEFIT?
d) DETERMINE THE TIME INVOLVED AND CHANGE TO DOLLARS AND CENTS.
Real estate taxes for the calendar year are $360 and have been paid in full. Settlement and closing takes place on September 1. Who gets credit for tax and for how much?
Closing taking place on July 1 and taxes for the calendar year are not due until November 1. Taxes are $1,200 for the year.
Who gets credit and for how much?
TYPES OF EXPENSES TO BE PRORATED
I. ACCRUED. Accrued by seller, but not paid. CREDIT to BUYER.
II. PREPAID. Prepaid by seller, but not fully used at closing. CREDIT to SELLER.
1. If the taxes are owed but not yet due, calculate the time that seller has owned the property and credit this time to buyer.
2. If taxes have been PREPAID for a period beyond the closing, seller will get a CREDIT for the time he will not own the property during the tax year.
TRUE: Generally seller is responsible for the day of the closing. However, in some cases, when the closing is on the first of the month, seller is only held responsible up to the last day of the preceding month.
...
PRORATING FIRE INSURANCE PREMIUMS (HAZARD INSURANCE)
Fire insurance policies may be written for 1, 3 or 5 years and are usually paid in advance to take advantage of reduced yearly rates. When property is sold and the policy is transferred (assigned) the buyer will owe the seller for the unearned premium (paid for but not used).
Ex: Closing date is September 20, 1975. A 3-year fire insurance policy written August 12, 1974 will be transferred to buyer. Paid up 3-year premium is $300. How much credit is due seller?
PRORATION OF MORTGAGE INTEREST
When a mortgage is taken over (or assumed) at the closing, the accrued interest due will have to be prorated. Interest on the mortgage is usually paid in arrears for the period of time preceding day of payment. It is important to determine at the closing whether interest is due up to, and including, the day of the payment or up to, but not including the day of the payment.
Example of interest paid up to and including day of payment.
Buyer will assume a mortgage with a balance due of $12,000 @ 6% per annum. Interest is paid monthly, with the last payment being paid on March 1, including interest for that day. Closing is March 22. How much interest will be due buyer?
Example of interest paid up to, but not including day of payment.
Balance due on mortgage is $12,000 @ 6% per annum and is paid quarterly. The last mortgage payment was made July 1 including interest for the month of June. Closing date is August 15. How much will we credit buyer?
EXCHANGE OR BOOT PROBLEMS
Exchanging properties of a like kind is a method by which an investor can reduce, defer, and even eliminate capital gains tax. The amount of cash which is required to even out an exchange is referred to as "boot".
For example, if Able exchanges his home which is worth $40,000 for Brown's house which is worth $60,000, and there are no liens or mortgages on either property, Able would owe Brown $20,000 in boot. The amount of equity (price less mortgage) being exchanged determines the boot. For example: Carter wants to trade his home valued at $67,000 with a remaining mortgage of $30,000 for a home valued at $96,000 with a mort- gage balance of $50,000. Besides his house, what cash to boot must Carter give to obtain the other home?
THE BOX FORMULA
Type of Problem: Commission
Rate:
Principal:
Earnings:
Type of Problem: Loan Interest
Rate: Interest Rate
Principal: Loan Amount
Earnings: Annual Interest
Type of Problem: Depreciation
Rate: Depreciation Rate
Principal: Cost
Earnings: Depreciation
Type of Problem: Profit & Loss
Rate: Rate of P or L
Principal: Cost
Earnings: Profit or Loss
Type of Problem: Capitalization
Rate: Cap. Rate
Principal: Investment
Earnings: Net Return
Type of Problem: Return on Investment
Rate: Rate of Return
Principal: Investment
Earnings: Net Return
STRATEGY FOR SOLVING WORD PROBLEMS
1. Read the problem carefully and thoroughly.
2. Determine what the question is. What is the missing variable?
3. Pick out the known variables and label them.
4. Place the known variables in the formula and do the operation indicated.
4. Place the known variables in the formula and do the operation indicated.
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