Real Estate Math Example Problems
What is the rate of interest if the borrower makes quarterly interest payments of $1,115.63 on an $85,000 loan?
$1,115.63x4= $4,462.52 $4,462.52/85,000=5.25%
An office building produces $132,600 annual gross income. If the annual expenses are $30,600 and the appraiser estimates the value using an 8.5% rate of return, what is the estimated value?
$132,600-$30,600= $102,000 NOI $102,000/8.5%= 1,200,000
If a property is assessed for tax purposes at $160,000 with an equalization factor or 80% is taxed at a rate of 30 mills, what will the tax amount be on the property?
$160,000x80%= $128,000 $128,000x.03= $3,840
If a buyer has a loan of $175,000 and the lender uses a loan payment factor of 6.32 per $1,000 of the loan amount, what will be the monthly principal and interest payment?
$175,000/1,000x6.32= $1,106
If an investment valued at $450,000 returns 12% annually, then what is the amount of income produced?
12%x$450,000=$54,000 income
Kim's commission on a sale that was $12,500 which was 4% of the sales prices. What was the sales price?
12,500/4%= $312,500`
Fencing comes in 5 foot sections. For a fence that is 120 feet long, how many fence posts are needed?
120/5=24 24+1= 25 (post for the end)
$175 is 3.5% of what amount?
175/3.5%= $5,000
The value of a house without the lot at the end of 4 years is $132,300. What was the original cost of the house if the yearly rate of depreciation is 2.5%?
2.5x4= 10 100%-10%= 90% $132,300/90%=$147,000
A savings and loan agreed to make a $75,000 mortgage at 4% interest for 30 years. They charged 3 points on the loan. What was the effective yield to the lender?
3 points= 3x1/8%(.125)=.375% 4%=.375%= 4.375% effective yield
A borrower is closing on an $114,300 loan with an interest rate of 6.75% on November 18. How much interim interest will be due at closing? The first full payment is due January 1st.
30 days in Nov.- 18(days until closing)= 12 days + 1 (day of closing)= 13 days $114,300x6.75%= $7,715.25 annual interest $7,715.25 /360= $21.43125 interest per day $21.43125x13= $278.61
A parcel sold for $335,200. The lender granted a 90% loan at 7.5% for 30 years. The appraised value is $335,500. How much interest is paid in the first monthly payment?
335,200x90%= $301,680 is the loan amount 301,680x7.5%= 22,626 22,626/12= $1,886.50 monthly payment
A building is 40 feet x 25 feet with a 10 foot high ceiling. It has a gable roof that is 8 feet high at the tallest point. How many cubic feet is the building?
40x25x10= 10,000 cubic feet in the building 40x25x8/2= 4,000 cubic feet in gable roof 10,000+4,000= 14,000 cubic feet
A lot contains 9/10 of an acre. What is the depth of the lot if the front measures 150 feet?
43,560x .9= 39,204 39,204/150= 261.36
A 5 acre lot had a front footage of 300 feet. How deep is it?
43,560x5= 217,800 217,800/300= 726 feet
Carpet costs $63 per square yard, what would it cost to carpet a room 476.625 sq ft?
476.625/ 9= 52.958333 (9 ft= sq yard) 52.958333x $63= $3,336.38
After deducting $5,850 in closing costs and 5% brokers commission, the seller receives their original cost of $175,000 plus $4,400 profit. What was the sales prices?
5,850 + 175,00 + 4,400= 185,250 income 95% after commission 185,250/95%= $195,000 sales price
A building is 500 feet long, 400 feet wide, and 25 feet high. How many cubic feet is the building?
500x400x25= 5,000,000
An a-frame cabin is 50 feet long and 30 feet wide. The cabin is 25 feet high from the base to the highest point. How many cubic feet?
50x30x25/2= 18,750 cubic feet
A two story house measures 58 ft x 30 ft and costs $85 per square foot to build. What is the construction cost?
58x30= 1,740 1,740x2= 3,480 3,480x85= $295,800
How many cubic yards of concrete would it take to build a sidewalk measuring 120 ft long, 2 feet 6 inches wide and 3 inches thick?
6 inches/12= .5+2= 2.5 ft wide 3 inches/12= .25 inches thick 120x2.5x.25= 75 cubic feet 75 cubic ft/ 27 cubic ft= 2.778 cubic yards
How many square feet are in a room 15'6"x 30'9"? (inches-> feet)
6"/12= .5 ft + 15'= 15.5' wide 9"/12= .75 ft + 30 ft= 30.75' long 20.75x15.5= 476.625 sq ft
Morris negotiated a $60,000 loan with $400 monthly payments plus 9% interest. What us the monthly interest?
60,000x9%= $5,400 $5,400/12= $450 monthly interest
A home sells for $180,000 and has a 7% commission. What is the amount of commission?
7%x180,000= $2,600
7 years ago you purchased a piece real estate for $93,700 including the original cost of the land, $6,700. What is the value of the land today using n appreciation rare of 8%/year?
8%x7 years= 56% 100%+56%= 156% $6,700x 156%= $10,586 land value
The lender will charge 3.5 loan discount points on an $80,000 loan. What will be the total amount due for points?
80,000x3.5%= $2,800
You invest $335,000 in a property that should produce a 9% rate of return. What monthly NOI will you receive?
9%x$335,000= $30,150 $30,150/12= $2512.50
A seller lists a home for $200,000 and agreed to pay a full commission rate of 5%. The home sold for 90% of the list price. The listing broker agreed to give the selling broker 50% and the salesperson 60%. How much commission did the salesperson receive?
90%x200,000= 180,000 180,000x 5%= $9,000 $9,000/2- $4,500 $4,500x60%= $2,700 commission to salesperson
Matt owns a lot measuring 90 ft x 130 ft. The county puts in a new street on the front side of his home and assesses him 8 cents per square foot. What will the new street cost him?
90x130=11,700 11,700x.08= $936
Dave wants to decorate his home, so he got a loan of $5,300 at a rate of 6%. He paid off his loan in 8 months. What was the total amount of interest Dave paid?
$5,300x6%= $318 $318x8=2,544 $2,544/12= $212 in interest
If a house sold for $60,000 and the buyer got an FHA insur3ed loan for $58,700, how much money would the buyer pay in discount points if the lender charged 4 points?
$58,700x4%= $2,348
If a borrower must pay $7,500 for points on a $150,000 loan, how many points is the lender charging?
$7,500/$150,000= 5 points
A lease calls for a monthly minimum rent of $900 plus 3% of annual gross sales in excess of $270,000. What was the annual rent in a year when the annual gross sales were $350,600?
$900x12= $10,800 minimum 350,600-270,000= $80,600 80,600x3%= $2,418 $2,418+ $10,800= $13,218 annual rent
A parcel of land is described as "the NW 1/4 of the SW 1/4 of section 6, T4N, R8W of the Third Principal Meridian" was sold for $875 per acre. The listing broker will receive 5% commission on the total sales price. How much will the broker receive?
1 section= 640 acres NW 1/4= 160 acres SW 1/4= 160 acres 320 acres x $875= $280,000 $280,000x 5%=$14,000
Bev bought her home in Echo Hills one year ago for $138,500. Property in her neighborhood is said to increasing in value at a rate of 3% annually. What is her home worth now?
100%+3%=103% $138,500x103%=$142,655
You just sold your cabin for $80,640 losing 16% of your investment. What was the original cost?
100%-16%=84% $80,640/84%=$96,000
A building that costs $350,000 to construct 9 years ago has depreciated 25%. The land costs $65,000, what is the appraised value?
100%-25%- 75% $350,000x75%=$262,500 $262,500+$65,000= $327,500 appraised value
Your home listed for $285,000 and sold for $275,000, which gave you a 10% profit over the original cost. What was the original cost?
100%=10%=110% $275,000/110%=$250,000
If the transfer taxes are payable at the rate of 55 cents per $500 or part thereof, what is the grantor's cost on a $49,750 sale?
$49,750/500= 99.5 round up to 100 100x.55= $55
If a buyer has a loan of $301,680 and the lender uses a loan payment factor of 6.99 per $1,000 of the loan amount, what will be the monthly principal and interest payment?
$301,680/1,000x6.99= $2,108.74
If the annual net income from a commercial property is $33,000 and the capitalization rate is 9%. What is the value of the property using the income approach?
$33,000/9%=$366,666,67
If Edna's property is valued at $35,000, is assessed at 50% of its value and the mill levy is 79, what is Edna's annual taxes?
$35,000x50%= $17,500 $17,500x.079= $1,382.50
What is the annual real estate tax on a property valued at $135,000 and assessed for tax purposes at $47,250 with an equalization factor of 125%, when the tax rate is 25 mills?
$47,250x125%= $59,061.50 $59,061.50x .025= $1,476. 56
