RFINANCE18: Finance Math

Here's the correct calculation:

Break-even = Fixed costs ÷ (1- Variable cost ratio) Break-even = $100,000 ÷ (1 - 0.20) Break-even = $100,000 ÷ 0.80 Break-even = $125,000 30,000 sq. ft. x $5 = $150,000 $125,000 ÷ $150,000 = 0.8333 = 83 percent occupancy needed to break even

Break even Analysis: Your Turn

Calculate the break-even point and percent of occupancy needed to break even for the following project: Fixed cost - $100,000 per year Variable cost ratio - 20 percent per rental dollar 30,000 square feet of rentable space $5 per square foot per year

Summary/Review:

From a buyer's perspective, interest can be defined as the amount paid in return for the use of money. From the lender's perspective, interest is money earned or received from a loan investment. Simple interest is money that is paid only for the amount of principal the borrower still owes. Compound interest is defined as interest which is computed on the principal amount plus the accrued interest. Points are a one-time service charge to the borrower for making the loan. There are two types of points: Origination points Discount points Points represent prepaid interest and the lender charges them to get additional income on the loan. Points are paid at closing and are usually equal to 1 percent of the loan amount. Borrowers are responsible for making monthly mortgage payments, which include both principal and interest. The lender runs an amortization schedule that is based on the amount of the loan, the term of the loan and the interest rate. Most real estate mortgage loans are based on simple interest.

Calculating Income and Debt Ratios:

Gary and Sue want to purchase a home for $92,000. Here are the facts, along with how the lender will calculate the income ratio. Total amount of new house payment: $900.00 Gary and Sue's gross monthly income: $4,000.00 Divide total house payment by gross monthly income: $900 ÷ $4,000 Income ratio: 22.5% Now here's how the lender will calculate the debt ratio. Total amount of new house payment: $900.00 Total amount of monthly recurring debt: $725.00 Total amount of monthly debt: $1,625.00 Gary and Sue's gross monthly income: $4,000.00 Divide total monthly debt by gross monthly income: $1,625÷$4,000 Debt ratio: 40.62%

Let's do the calculation for the second month of Julie and Bob's mortgage:

Here's the calculation for the third month of Julie and Bob's mortgage. Current loan balance $89,811.61 Rate is 5.75 percent per year Monthly payment is $525.22 $89,811.61 x .0575 = $5,164.17 yearly interest $5,164.17 ÷ 12 = $430.35 third month's interest $525.22 - $430.35 = $94.87 third month's principal New balance for next month's calculation. $89,811.61 - $94.87 = $89,716.74

Points Let's do some calculations:

Mark and Amy are getting a $120,000 loan at 8.5 percent and will pay 2 origination points at closing. What will the point cost be and what will the effective interest rate be? Point cost: $2,400 $120,000 x .01 x 2 points Effective interest rate: 8.5 percent (Origination points do not change the effective rate of the interest.) But what if the lender were charging 2 discount points instead of origination points? How would that change the figures? The calculation for the point amount remains the same. Point cost: $2,400 $120,000 x .01 x 2 points But now let's look at how the rate changes. 2 points x 1/8 percent = 2/8 = .25 percent 8.5 + .25 = 8.75 percent effective rate

Simple Interest:

Most real estate loans use simple interest. Simple interest is money that is paid only for the amount of principal the borrower still owes. When the money is repaid to the lender, the payments stop. The formula for computing simple interest is: Interest = principal x rate x time Using the formula above, the interest rate on a $2,250 loan for one year at 7 percent interest is $157.50. $2,250 x .07 x 1 = $157.50 This loan will be paid in 12 equal monthly installments of $187.50, plus the simple interest at the 7 percent rate. The first month's interest will be computed on the full loan of $2,250. However, the second month's interest will be computed on the new loan balance of $2,062.50, which is the original $2,250 minus the monthly principal of $187.50. As we said earlier, simple interest is calculated only on the remaining loan balance. We'll have more examples of the simple interest calculation when we talk about amortizing mortgage payments later in this unit.

Points Your Turn:

Points Here are the answers. Laura is getting an $85,000 loan at 7 percent and will pay 3 origination points. What will the point cost be and what will the effective interest rate be? Point cost: $2,550 $85,000 x .01 x 3 points Effective interest rate: 7 percent (Origination points do not change the effective rate of the interest.) Bill and Jenna are getting a $175,000 loan at 8 percent and will pay 4 discount points. What will the point cost be and what will the effective interest rate be? Point cost: $7,000 $175,000 x .01 x 4 points Effective interest rate: 8.5 percent 4 points x 1/8 percent = 4/8 = .50 percent 8.0 + .50 = 8.5 percent Hal is getting a $65,000 loan at 9 percent and will pay 2 discount points. What will the point cost be and what will the effective interest rate be? Point cost: $1,300 $65,000 x .01 x 2 points Effective interest rate: 9.25 percent 2 points x 1/8 percent = 2/8 = .25 percent 9.0 + .25 = 9.25 percent Neil and Jennifer will get a $285,000 loan at 7.5 percent and will pay 1 origination point and 2 discount points. What will the point cost be and what will the effective interest rate be? Point cost: $8,550 $285,000 x .01 x 3 points (They are paying 3 total points.) Effective interest rate: 7.75 percent 2 points x 1/8 percent = 2/8 = .25 percent (Only 2 of the 3 points are discount points.) 7.5 + .25 = 7.75 percent

Answers More Proration Math:

Proration Math The 365-day method calculates the amounts on the basis of a 365-day year. Identify an item and the amount needing to be prorated. Divide by 365 to get the daily rate. (Divide by 366 in a leap year.) Multiply the daily rate by the number of days the seller owned the property before closing to get the seller's share. Subtract the seller's prorated amount from the starting amount to get the buyer's prorated amount. Let's look at an example using this method. Buyers Greg and Jane have arranged to take over Al and Kathy's insurance policy. The premium is $550 per year paid in advance on March 1. Closing on the property is set for June 11. What is Al and Kathy's share of the insurance cost? Total amount: $550.00 Daily amount ($550 ÷ 365) $1.51 Al and Kathy's share = $155.53 $1.51 x 103 days (March 1 through June 11) = $155.53 Greg and Jane's share = $394.47 $550 - $155.53 = $394.47 Since Al and Kathy paid the premium in advance, Greg and Jane's share of $394.47 will be credited to the sellers and debited to the buyers.

Computing Payments Using the Add-On Interest Rate Method:

To briefly look at how to calculate an add-on interest rate payment, you use the simple formula: (Total principal + Total Interest) ÷ Number of payments = Periodic payment Let's take a $100,000 loan @5% for 3 years (36 payments). First we'd compute the total interest for the year. $100,000 x .05 x 3 years = $15,000 Then we add the interest amount to the total loan amount. $100,000 + $15,000 = $115,000 total amount repayable Finally, divide the total amount payable by the total number of payments to derive the monthly payment amount. $115,000 ÷ 36 = $3,194.44 Using this method, the borrower pays the same $3,194.44 payment every month for the 36 months.

Identifying the Monthly Payment Using the Add-on Interest Rate Method Your Turn:

Using the data presented, compute the monthly payments using the add-on interest rate method. Then move to the next screen to check your work. $30,000 @ 6% @ 1 year = _____ $40,000 @ 5% @ 2 years = _____ $60,000 @ 4% @ 3 years = _____ Here are the correct answers. $30,000 x .06 x 1 year = $1,800 total interest ($30,000 + 1,800) ÷ 12 months) = $2,650 / month $40,000 x .05 x 2 years = $4,000 total interest ($40,000 + 4,000) ÷ 24 months = $1,833 / month $60,000 x .04 x 3 years = $7,200 total interest ($60,000 + $7,200) ÷ 36 months = $1,867 / month

Commercial Projects:

- An important aspect of investing is the ability to measure the profitability of an investment. As we discussed in a previous unit, in order to determine profitability, an analyst must do an accurate estimate of the stream of income expected for the particular property over a specified period of time. - When deciding to make a commercial loan, a lender will thoroughly examine the borrower's financial liquidity to determine his or her ability to make the payments. The lender will also assess the profitability of the specific project as to its ability to generate cash flow necessary to be successful financially. The loan analyst will be most interested in the project's break-even point and its return on investment, as well as some other variables.

Calculating Income and Debt Ratios:

- As we discussed in an earlier unit, lenders will try to estimate a potential borrower's ability to fulfill the loan obligation by establishing an income ratio and a debt ratio. - To review, the income ratio establishes the borrower's capacity to pay the loan by limiting the percent of gross income he or she may spend on housing costs. Housing costs include the principal, the interest, the taxes and homeowner's insurance, and also may include some monthly assessments for mortgage insurance and utilities. Conventional loans typically require this ratio to be under 28 percent. FHA guidelines require the income ratio to be no more than 29 percent. - A borrower's debt ratio is calculated based on all of the monthly obligations the borrower has, including those items or payments the borrower must make for other debts. These debts could be such items as car payments and revolving charge accounts. Conventional loans usually require the debt ratio be 36 percent or lower, but FHA guidelines state the debt ratio may not be greater than 41 percent.

Points:

- As we discussed in an earlier unit, points are items usually included in the cost of obtaining a new real estate loan. Points are a one-time service charge to the borrower for making the loan. - There are two types of points: Origination points Discount points - Points represent prepaid interest, and the lender charges them to get additional income on the loan. Points are paid at closing and are usually equal to 1 percent of the loan amount. Two (2) points on a $75,000 loan would be $1,500. ($75,000 x .01 x 2 points) - Origination Points Lenders charge origination points to recover some costs of the loan origination process. In many cases, a loan officer's compensation is based on the origination points. Depending on the lending institution, the origination points may be negotiable. - Discount Points These charges are designed to offset any losses the lender might suffer when selling the loan to the secondary mortgage market. Discount points are a means of raising the effective interest rate of the loan. The rule of thumb is 1/8 percent for each discount point. So a charge of 4 points would increase a 7.25 percent mortgage to a 7.75 percent yield. 4 points x 1/8 percent = 4/8 = .50 percent 7.25 + .50 = 7.75 percent

Break-even Analysis:

- Break-even analysis is the chief method used to estimate the potential profitability of a real estate investment. This involves determining the investment's break-even point, which is the point at which the gross income is equal to a total of the fixed costs, plus all of the variable costs that were incurred to generate the gross income. A project will begin to show a profit only when the gross income is higher than the amount required to break even. - Every real estate investment project has fixed costs that are always there, regardless of the income. These costs can include property taxes, insurance premiums, loan payments, and basic property maintenance and utility charges that must be paid out, even when there is no income. - A real estate investment project also has variable costs that rise and fall in proportion to the income it generates. These costs include salaries for managers, specialized maintenance services, bookkeeping and advertising. Variable costs are usually expressed as a ratio of rental income, such as 20% for every dollar of income collected, and are applied at a set rate for any level of income.

Proration Math:

In an earlier unit, we discussed in detail the HUD Form-1 used in closing transactions. As you remember, some expenses paid at closing must be prorated or divided proportionately between the buyer and the seller. The most common items that fall into this category include Taxes Insurance Mortgage interest Utilities Any item that is prorated is shown on the settlement statement as a debit to one party and a credit to the other party for the same amount. Some items are those that were paid for in advance, so the buyer will owe the seller part of the payment. For example, let's say the seller paid real estate taxes for the first half of the fiscal year in advance and the transaction will close on September 18. The buyer will owe the seller the portion of the taxes that apply from September 19 to December 31. Note: In California, property taxes are paid on a fiscal year basis beginning on July 1st and ending on June 30th of the following year. The taxes are billed in two installments. The first half is due November 1 and the second half is due February 1. However, the homeowners can pay the taxes in full for the entire year any time after they receive the bill. Or if the seller paid for the rental of a propane tank for the calendar year, the buyer will owe the seller the prepaid rent on the tank from September 19 to December 31. For items paid in advance, the buyer will receive a debit and the seller will receive a credit. Other items are those expenses that the seller incurred but have not yet been billed for at the time of closing. These items are paid in arrears. For example, the buyer will receive the sewer bill for September. The charges from September 1-18 belong to the seller, but the buyer will be paying the bill. So on the settlement statement, the buyer will get a credit and the seller will get a debit.

More Proration Math::

Jim and Beth have sold their single-family residence to Tim and Sue and are closing on May 17. The annual real estate taxes for the property are $1,950. What is Jim and Beth's share of the annual taxes? What is Tim and Sue's share? (Remember, California bills taxes on a fiscal year basis and in two installments, so in this case, the July 1 - December 31 tax installment has already been paid by the sellers.) Total amount: $1,950.00 Semi-annual amount ($1,950 ÷ 2) $975.00 Monthly amount ($975 ÷ 6) $162.50 Daily amount ($162.50 ÷ 30) $5.42 Jim and Beth's share of annual taxes = $1717.14 1st paid installment = $975 $162.50 x 4 months (January through April) = $650 $5.42 x 17 days (May 1 through 17) = $92.14 (975 + 650 + 92.14) = $1717.14 (5. Jim and Beth's 2nd installment share = (650 + 92.14) = $742.14) Tim and Sue's share = $232.86 (1950 - 1717.14) = $232.86 Note: If the seller prepaid the taxes when billed on February 1, the buyer's share of $232.86 will be shown as a credit to the seller and a debit to the buyer. However, if the seller had not yet paid the 2nd installment of the taxes, the seller's share of $742.14 will be shown as a debit to the seller and a credit to the buyer, since the buyer will have to pay the entire $975.

Summary/Review::

Lenders will try to estimate a potential borrower's ability to fulfill the loan obligation by establishing an income ratio and a debt ratio. Conventional loans typically require the income ratio to be under 28 percent and the debt ratio to be 36 percent or lower. FHA guidelines require the income ratio to be no more than 29 percent and the debt ratio no more than 41 percent. Some expenses paid at closing must be prorated or divided proportionately between the buyer and the seller. Any item that is prorated is shown on the settlement statement as a debit to one party and a credit to the other party for the same amount. Closing agents and lenders typically use one of two methods when calculating items that need to be prorated: the 12- month/360-day method and the 365-day method. When deciding to make a commercial loan, a lender will thoroughly examine the borrower's financial liquidity and assess the profitability of the specific project. The loan analyst will be most interested in the project's break-even point and its return on investment (ROI). The breakeven point is the point at which the gross income is equal to a total of the fixed costs, plus all of the variable costs that were incurred to generate the gross income. The return on investment is the ratio of pre-tax net income to the money invested. Real estate lenders often use a required return on an investment, called a capitalization rate, as the means for estimating the value of the collateral being pledged for a loan.

Computing Compound Interest:

Let's compute the compound interest for a $5,000 savings account left in the bank for 5 years at 5 percent, compounded annually. Compound amount = Initial deposit (1 + Interest rate)n Compound amount =$5,000 (1 + .05)5 Compound amount =$5,000 (1.05)5 In this next step, 1.05 gets multiplied by itself 5 times. 1.05 x 1.05 x 1.05 x 1.05 x 1.05 = 1.2762 Compound amount =$5,000 x 1.2762 Compound amount = $6,381.00 Note: If the interest gets compounded more often than once a year, the effective rate would be a bit higher than the nominal rate. For example, a deposit that has a 6 percent annual rate might have an effective rate of 6.06 percent if the interest is compounded more frequently than once a year. Since savings accounts with compound interest are safe investments, investors often use them to help in making investment decisions. The investor compares the rate of return on a compounded savings account with the possible rate of return on other alternative investments to help assess the risks involved.

Your Turn Again:

Sally and Dan obtain a mortgage for $145,000 for 30 years at a fixed rate of 8.75 percent. When the lender runs the amortization calculation, the result will produce a monthly payment amount of $1,140.72. Calculate the allocation of principal and interest for the first five payments. Then calculate the total amount of principal and the total amount of interest Sally and Dan paid in the first five months. When you're finished, go to the next screen to check your work. Here are the correct calculations. Month 1 $145,000 x .0875 = $12,687.50 yearly interest due $12,687.50 ÷ 12 = $1,057.29 first month's interest $1,140.72 - 1,057.29 = $83.43 first month's principal Month 2 $145,000 - $83.43 = $144,916.57 new balance $144,916.57 x .0875 = $12,680.20 yearly interest $12,680.20 ÷ 12 = $1,056.68 second month's interest $1,140.72 - $1,056.68 = $84.04 second month's principal Month 3 $144,916.57 - $84.04 = $144,832.53 new balance $144,832.53 x .0875 = $12,672.85 yearly interest $12,672.85 ÷ 12 = $1,056.07 third month's interest $1,140.72 - $1,056.07 = $84.65 third month's principal Month 4 $144,832.53 - $84.65 = $144,747.88 new balance $144,747.88 x .0875 = $12,665.44 yearly interest $12,665.44 ÷ 12 = $1,055.45 fourth month's interest $1,140.72 - $1,055.45 = $85.27 fourth month's principal Month 5 $144,747.88 - $85.27 = $144,662.61 new balance $144,662.61 x .0875 = $12,657.98 yearly interest $12,657.98 ÷ 12 = $1,054.83 fifth month's interest $1,140.72 - $1,054.83 = $85.89 fifth month's principal Total Principal Paid: $423.28 Total Interest Paid: $5,280.32

Here are the correct answers:

Sally and Sam have sold their home to Tina and Max. The closing is set for August 23. The yearly real estate taxes are $1,700 and the first installment has not yet been paid. Using the 12 month/30 day method, what will be Sally and Sam's share of the taxes and how will they be handled on the settlement statement? $1,700 ÷ 12 = $141.67 $141.67 ÷ 30 = $4.72 Seller's portion - $141.67 x 1 = $141.67 (July) $4.72 x 23 = $108.56 (August 1-23) $141.67 + $108.56 = $250.23 will be a debit to the seller and a credit to the buyer Paul, the buyer, will get the second quarter water bill at the end of June. The bill is $39.00 per quarter. If closing is on May 7, what will be Paul's share of the bill? $39 ÷ 91 days = $.43 per day $.43 x 54 days (Paul's share of the 91 days) = $23.22

What Is Interest?

- The types of math problems normally seen in real estate finance include identifying amounts of principal, interest, loan payments, property taxes, income taxes, insurance premiums, assessment charges, appreciation, discounts, and returns on investments. - In residential transactions, most buyers are concerned with how much of a down payment they will need and what the monthly payments will be, so that they can determine whether or not they will be able to afford the property. Buyers will also evaluate the total price of the property, how much interest they would be paying on the loan overall and the amount of the property taxes and insurance premiums they will have to pay. - In commercial property transactions, principals have all the same concerns as stated above, plus concerns about cash flow, break even points, and investment returns. Before we get too heavily involved in computations, let's first look at the definition of interest. (del) One of the foundations of real estate finance is the concept of interest. From a buyer's perspective, interest can be defined as the amount paid in return for the use of money. From the lender's perspective, interest is money earned or received from a loan investment. So we can say that real estate finance is the process in which interest and principal are paid and received under the terms and conditions of a loan agreement. The money is borrowed at a certain rate of interest for a specific time frame, during which the borrower repays the amount borrowed.

Add on Interest:

Although most real estate loans use the simple interest method, some lenders occasionally use what's called an add-on rate. This method entails computing the interest on the total amount of the loan for the entire loan term. Then this amount of interest is added to the total principal amount before the monthly payments are calculated. Lenders use this interest computation method for some home improvement loans and many private mortgage companies use it for junior liens. Add-on interest almost doubles the simple interest rate. The formula for computing the add-on interest rate is: AIR = 2 x I x C ÷ P (n + 1) or Add-on Interest Rate = 2 x number of Installment payments per year x total loan Charge ÷ Principal x the sum of the number of installments in the contract + 1 Let's use our same numbers from our simple interest example (loan of $2,250 at 7 percent for 1 year) to do the computation using the add-on method. First we'd compute the total interest for the year like we did earlier. $2,250 x .07 x 1+ $157.50 Then we add the interest amount to the total loan amount. $2,250 + $157.50 = $2,407.50 Lastly we divide the new total loan amount by the number of payments to get the monthly payment amount. $2,407.50 ÷ 12 = $200.62 Using this method, the borrower pays the same $200.62 payment every month for the 12 months. So even though the first month's payment actually reflects the 7 percent simple interest rate, for the remaining eleven months, the borrower is paying more in interest each month as the principal balance decreases.

Calculating Mortgage Payments:

Although some real estate loans can be repaid annually, the most common repayment plan is monthly. As we know, a borrower is responsible for making those monthly payments, which include both principal and interest. Most typically, the borrower has a flat monthly payment, part of which goes to interest and the rest to principal. So how does the lender determine how much to allocate to interest and how much to principal? In the case of amortized loans, the lender calculates an amortization schedule that is based on the amount of the loan, the term of the loan and the interest rate. The amortization calculation produces a monthly payment amount. For example, Julie and Bob obtain a mortgage for $90,000 for 30 years at a fixed rate of 5.75 percent. When the lender runs the amortization calculation, the result will produce a monthly payment amount of $525.22. Using the example above, let's see how the lender allocates the interest and principal. Loan is $90,000 Rate is 5.75 percent per year Monthly payment is $525.22 $90,000 x .0575 = $5,175 yearly interest due $5,175 ÷ 12 = $431.25 first month's interest $525.22 - $431.25 = $93.97 first month's principal Now the lender will subtract the principal payment from the initial loan balance to arrive at the loan balance for next month's calculation. $90,000 - $93.97 = $89,906.03

Return on Investment:

Another percentage measure of profitability is the return on investment (ROI), which is the ratio of pre-tax net income to the money invested. For example, a deposit of $10 in a savings account at 6 percent interest will develop a $.60 return on the $10 invested that year. In the same way, a $2.00 return on the $10 investment would have a 20 percent ROI. Real estate lenders often use a required return on an investment as the means for estimating the value of the collateral being pledged for a loan. This required return is called a capitalization rate and is usually applied on the net income before taxes. Lenders estimate an income property's value from its capitalization rate using the following formula: Value = income ÷ rate For example, if a property has a $50,000 net annual cash flow and capitalization rate of 10 percent, here is how we would calculate its value. Value = income ÷ rate Value = $50,000 ÷ .10 Value = $500,000 Keep in mind that the formula above can be rearranged to find any of the values, if the other two are known. Here are the other two formulas. Rate = Income ÷ Value Rate = $50,000 ÷ $500,000 Rate = 10 percent Income = Value x Rate Income = $500,000 x .10 Income = $50,000

Break-even point is calculated using this formula:

Break-even = Fixed costs ÷ (1- Variable cost ratio) For example, here is how we would calculate the gross income needed to break even on a property that has a fixed cost requirement of $150,000 annually and a variable cost ratio of 25% per rental dollar. Break-even = Fixed costs ÷ (1- Variable cost ratio) Break-even = $150,000 ÷ (1 - 0.25) Break-even = $150,000 ÷ 0.75 Break-even = $200,000 If this project has 50,000 square feet of rentable space at a rent of $6 per square foot per year, the project will break even when 67 percent of the space is rented. 50,000 sq. ft. x $6 = $300,000 $200,000 ÷ $300,000 = 0.6666 = 67 percent A break-even analysis such as this gives the lender and the investor a good idea of how economically feasible the project is. In the above example, the break-even point seems to be quite reasonable, so the project would probably get the go ahead from the lender. If however, the project needed a much higher occupancy rate in order to break even, the lender and investor both would probably decide not to pursue it.

Return on Investment: Your Turn

Calculate the following problems. When you're finished, move to the next screen to check your work. What is the capitalization rate of a property that sold for $325,000 and is producing an annual net operating income of $29,250? A property valued at $350,000 has an annual net operating income of $43,750. What is the capitalization rate? A building is producing an annual net operating income of $17,050 and has a capitalization rate of 6.2%. What is the value of the building? If a building is producing an annual net operating income of $34,500 and the capitalization rate is 12%, what is the value of the building?

Calculating Simple Interest Amounts Your Turn:

Calculate the total interest due on the following loan amounts. Then move to the next screen to check your work. $3,000 loan at 6 percent for one year $4,200 loan at 5 percent for one year $6,500 loan at 9 percent for one year $7,275 loan at 8 percent for one year Here are the correct answers. $3,000 x .06 x 1 = $180 $4,200 x .05 x 1 = $210 $6,500 x .09 x 1 = $585 $7,275 x .08 x 1 = $582

More Proration Math:More

Closing agents and lenders typically use one of two methods when calculating items that need to be prorated: the 12- month/360 day method and the 365 day method. The 12 month/30 day method calculates the amounts due based on a 360-day year and a 30-day month. The steps of this method are as follows. Identify an item and the amount needing to be prorated. Divide by 12 to get the monthly rate. Divide by 30 to get a daily rate. Multiply the monthly rate by the number of months the seller owned the property before closing to get the months-amount due. Multiply the daily rate by the number of days the seller owned the property in the closing month to get the amount due for the closing month. Add the two amounts to get the prorated amount for the seller. Subtract the seller's prorated amount from the starting amount to get the buyer's prorated amount.

Compound Interest:

Compound interest is defined as interest which is computed on the principal amount plus the accrued interest. At the beginning of a new interest period, all the accrued interest is added to the principal, forming a new principal figure on which the interest is then calculated. This process repeats itself each interest period. Interest may be compounded daily, monthly, semiannually or annually. For example, if a borrower gets a $1,000 savings account at 5 percent interest compounded annually, for the first year the amount of interest is $50. The $50 is now added to the $1,000 initial savings for a new balance of $1,050. The second-year interest is computed on the new balance of $1,050 and results in a second-year interest of $52.50. And so it goes. Compound interest is computed using the following formula: Compound amount = Initial deposit (1 + Interest rate)n Note: The n in the above formula equals the number of periods. When doing the calculation, the sum of 1 plus the interest rate gets multiplied by itself the number of times indicated by the n.

Let's do the calculation for the second month of Julie and Bob's mortgage.

Current loan balance $89,906.03 Rate is 5.75 percent per year Monthly payment is $525.22 $89,906.03 x .0575 = $5,169.60 yearly interest $5,169.60 ÷ 12 = $430.80 second month's interest $525.22 - $430.80 = $94.42 second month's principal Now subtract the principal payment from the loan balance to arrive at the balance for next month's calculation. $89,906.03 - $94.42 = $89,811.61 And so it continues. Each month the lender repeats the calculation to arrive at the new principal balance and allocate what part of the payment goes to interest and what to principal. Note: As small as the changes may be, you can see that, with each payment, the amount going to interest decreases while the amount going to principal increases.

Your turn:

Your Turn Complete these two proration problems and then move to the next screen to check your work. Sally and Sam have sold their home to Tina and Max. The closing is set for August 23. The yearly real estate taxes are $1,700 and the first installment has not yet been paid. Using the 12 month/30 day method, what will be Sally and Sam's share of the taxes and how will they be handled on the settlement statement? Paul, the buyer, will get the second quarter water bill at the end of June. The bill is $39.00 per quarter. If closing is on May 7, what will be Paul's share of the bill?

Landlords base their rents on the rental market of a particular property in a particular area. Lenders charge their rates of interest based on the current money market and the level of risk associated with a particular loan. There are several types of interest calculations. For our purposes, we'll discuss three of them:

Simple interest Add-on interest Compound interest

Return on Investment - Here are the answers:

What is the capitalization rate of a property that sold for $325,000 and is producing an annual net operating income of $29,250? Rate = Income ÷ Value Rate = $29,250 ÷ $325,000 Rate = .09 = 9 percent A property valued at $350,000 has an annual net operating income of $43,750. What is the capitalization rate? Rate = Income ÷ Value Rate = $43,750 ÷ $350,000 Rate = .125 = 12.5 percent A building is producing an annual net operating income of $17,050 and has a capitalization rate of 6.2%. What is the value of the building? Value = income ÷ rate Value = $17,050 ÷ .062 Value = $275,000 If a building is producing an annual net operating income of $34,500 and the capitalization rate is 12%, what is the value of the building? Value = income ÷ rate Value = $34,500 ÷ .12 Value = $287,500

Compound Interest Your Turn:

Compute the compounded amount for each of these savings accounts at various interest rates. Then go to the next screen to check your answers. $1,500 on deposit for 2 years at 5 percent, compounded annually $2,500 on deposit for 3 years at 4 percent, compounded annually $5,000 on deposit for 3 years at 6 percent, compounded annually $10,000 on deposit for 5 years at 5 percent, compounded annually Compound Interest Here are the correct answers. $1,500 on deposit for 2 years at 5 percent, compounded annually Compound amount =$1,500 (1 + .05)2 Compound amount =$1,500 (1.05)2 In this next step, 1.05 gets multiplied by itself twice. 1.05 x 1.05 = 1.1025 Compound amount =$1,500 x 1.1025 Compound amount = $1,653.75 $2,500 on deposit for 3 years at 4 percent, compounded annually Compound amount =$2,500 (1 + .04)3 Compound amount =$2,500 (1.04)3 In this next step, 1.04 gets multiplied by itself 3 times. 1.04 x 1.04 x 1.04 = 1.1248 Compound amount =$2,500 x 1.1248 Compound amount = $2,812 $5,000 on deposit for 3 years at 6 percent, compounded annually Compound amount =$5,000 (1 + .06)3 Compound amount =$5,000 (1.06)3 In this next step, 1.06 gets multiplied by itself 3 times. 1.06 x 1.06 x 1.06 = 1.1910 Compound amount =$5,000 x 1.1910 Compound amount = $5,955 $10,000 on deposit for 5 years at 5 percent, compounded annually Compound amount =$10,000 (1 + .05)5 Compound amount =$10,000 (1.05)5 In this next step, 1.05 gets multiplied by itself 5 times. 1.05 x 1.05 x 1.05 x 1.05 x 1.05 = 1.2763 Compound amount =$10,000 x 1.2763 Compound amount = $12,763