# How to Calculate Loan-to-Value Ratios and PMI in Residential Mortgage

The relationship of the loan amount to the value or sales price of the property securing the loan is called a loan-to-value ratio. The loan-to-value ratio (LTV) relates the loan to the lesser of the appraised value or sales price.

LTV = loan amount, divided by property value or sales price (whichever is less)

Or, shown another way:

Loan Amount                                     =     Loan-to-Value Ratio
Property Value or Sales Price (whichever is less)

 For Example The appraised value of a house is \$200,000, the sales price of the house is \$210,000, and the borrower has a \$25,000 down payment. The LTV can be calculated as follows:\$210,000 – \$25,000 = \$185,000. \$185,000 ÷ \$200,000 = 92.5%The LTV would be 92.5%.

The basic idea of LTV can be utilized for other purposes as follows:

 For Example A buyer wants to make an offer of \$190,000 on a property. He has \$6,000 available in earnest money. His lender will issue a 95% loan. The property is appraised at \$192,000. The loan amount can be calculated as follows:Loan = 95% x Sales Price (because sales price is less than the appraised value) \$190,000 x 0.95 = \$180,500The loan amount would be \$180,500.

 Note The earnest money does not affect the calculation of the loan. The earnest money will be applied to the down payment, so it is not considered at all when calculating the loan amount.
For Example
 For Example For a \$380,000 property, an applicant is offered a loan at 95% of the first \$250,000 of value and 90% of the value above \$250,000.The loan amount would be calculated in two steps: Calculate the loan on the first \$250,000 of value. Calculate the loan on the balance of the value above \$250,000, which is \$130,000 (\$380,000 – \$250,000). The total loan would consist of: 95% x \$250,000 =      \$237,500 90% x \$130,000 =   + \$117,000 Total Loan =              \$354,500

When a loan is more than 80 percent, the lender may require that the borrower purchase mortgage insurance. However, some lenders may charge a higher interest rate and not require the mortgage insurance regardless of the LTV, as in lender-paid mortgage insurance (LPMI). This was common practice during the subprime debacle and is not likely to be found today.

As an option, when the LTV exceeds 80 percent, a loan officer may offer two separate loans in such a fashion that neither loan will require mortgage insurance. These are called piggyback loans, or simultaneous seconds. The first loan will be for 80 percent of the loan value, and the second loan will cover the remainder.

If there will be two loans on the property, the ratio calculation remains the same except that the loan amount will be the sum of the first and second mortgages. This ratio is called a combined loan-to-value ratio (CLTV).

 Note: Under the Ability to Repay Rule, which went into effect in January of 2014, a creditor would have to ensure that the borrower had the ability to repay not only the first loan, but also any simultaneous loans securing the same property. This rule will be discussed in more detail later in this course.
For Example
A buyer wants to purchase a property with a sales price of \$300,000 and a down payment of \$20,000.

\$300,000 – \$20,000   = \$280,000
\$280,000 ÷ \$300,000 = 0.93
LTV  = 93%.

Because the LTV is more than 80 percent, the lender may offer two loans: one for \$240,000 and the other for \$40,000.

If there will be two loans on the property, the ratio calculation remains the same except that the loan amount will be the sum of the first and second mortgages.

1st Mortgage + 2nd Mortgage = Loan Amount
Sales Price

If a sales price is \$300,000, the down payment is \$25,000 and a second mortgage is \$35,000, the first loan will be \$240,000 (\$300,000 – \$60,000) and the resulting CLTV is:

\$240,000 + \$35,000 = \$275,000
\$300,000

CLTV = \$275,000 ÷ \$300,000 = 0.9166 = 91.7%.

In addition to the LTV and CLTV, with a home equity line of credit (HELOC), there is also a high combined loan-to-value ratio (HCLTV) and a total loan-to-value ratio (TLTV). When secondary financing is a HELOC, the loan balance plus any draw amount is used to calculate the CLTV. The loan balance plus the total line limit is used to calculate the HCLTV or TLTV.

 For Example A person has a house worth \$100,000 and an existing \$70,000 loan balance. He has a HELOC of \$20,000, of which he has drawn \$10,000.His LTV = \$70,000 ÷ \$100,000 = 70% His CLTV = \$80,000 (\$70,000 + \$10,000) ÷ \$100,000 = 80% His TLTV = \$90,000 (\$70,000 + \$20,000) ÷ \$100,000 = 90%

down payment is the difference between the purchase price and loan amount. It does not include closing costs. As a percentage, it is 100 percent of the price less the LTV or the CLTV. If the LTV is 80 percent, the down payment is 20 percent.

## Monthly Payments

An amortization schedule shows the schedule of individual annual or monthly payments over the term of a level payment loan. It includes the following:

• Payment
• Principal paid
• Interest paid
• Remaining balance

Amortization schedules can be produced by going online to any number of sites and providing the principal loan balance, the interest rate, the term of the loan and the starting month and year.

When such a schedule is not available, a monthly payment for an amortized loan may be determined in a number of ways. One is an amortization table. This shows the monthly payment amount of principal and interest, the loan term, the interest rate, and the original loan amount. It will not show the allocation of principal and interest, or the additional payments to tax and insurance reserves.

 10% Monthly Loan Amortization Payments 10% Loan Amount Term of Loan 3 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr 40 yr 100 \$ 3.23 \$ 2.13 \$ 1.33 \$ 1.08 \$ 0.97 \$ 0.91 \$ 0.88 \$ 0.85 200 6.46 4.25 2.65 2.15 1.94 1.82 1.76 1.70 500 16.14 10.63 6.61 5.38 4.83 4.55 4.39 4.25 1,000 32.27 21.25 13.22 10.75 9.66 9.09 8.78 8.50 5,000 161.34 106.24 66.08 53.74 48.26 45.44 43.88 42.46 10,000 322.68 212.48 132.16 107.47 96.51 90.88 87.76 84.92 15,000 484.01 318.71 198.23 161.20 144.76 136.31 131.64 127.38 20,000 645.35 424.95 264.31 214.93 193.01 181.75 175.52 169.83 25,000 806.68 531.18 330.38 268.66 241.26 227.18 219.40 212.29 30,000 968.02 637.42 396.46 322.39 289.51 272.62 263.28 254.75 35,000 1129.36 743.65 462.53 376.12 337.76 318.05 307.16 297.21 40,000 1290.69 849.89 528.61 429.85 386.01 363.49 351.03 339.66 45,000 1452.03 956.12 594.68 483.58 434.26 408.92 394.91 382.12

Amortization tables have, for the most part, been replaced by online and handheld financial (mortgage or real estate) calculators. The online calculators simply require entry of the loan amount, interest rate and loan term into the appropriate boxes to produce the monthly payment for a level payment mortgage loan. They are easy to find and operate.

A completed loan package for a borrower with a fixed loan rate will always contain an amortization table specific to the loan, showing the actual amount of interest and principal applied every month. It can be interesting to see how the amount of principal accrued increases gradually throughout the term because of the monthly payment remaining the same.

## Private Mortgage Insurance

Loans with an LTV higher than 80 percent generally require private mortgage insurance (PMI). The cost of this insurance varies based on the actual LTV and is expressed as an annual factor. For example, a loan between 80 percent and 85 percent might have a factor of 0.32 percent (or 0.0032), while a loan between 90 percent and 95 percent might have a factor of 0.0078.

To determine the monthly cost of the PMI, multiply the loan amount by the factor and divide by 12.

 For Example To calculate the PMI costs for a loan of \$200,000 that has a factor of 0.0032:\$200,000 x 0.0032 = \$640 annual PMI \$640 ÷ 12 months = \$53.33 monthly PMI

nterest rates can be reduced by paying prepaid interest at closing. This prepaid interest is called discount points or a buydown. The buydown money can come from the homebuilder or seller of the property; from the borrower; or from a third party, such as a relative, employer or investor.

There are two types of buydowns:

1. Permanent
2. Temporary

## What are Discount Points

A permanent buydown is a payment of discount points to lower the interest rate for the entire term of the mortgage. One discount point is equal to 1 percent of the loan amount. Therefore, a charge of 3 points on a \$100,000 loan would be \$3,000.

As a general rule, it costs about 6 discount points (6 percent of the loan amount) to reduce the interest rate by 1 percent. So if a borrower wanted to reduce his interest rate by a full 1 percent, he would have to pay 6 points, which would be an additional 6 percent of the loan amount. If he wanted to reduce his interest rate by one-half of a percent, he would need to pay 3 percent of the loan amount in points.

It is illegal to describe a point as a “discount point” without actually reducing the interest rate.

The actual cost of reducing the rate will vary from lender to lender, may fluctuate depending on market conditions, and will be limited in amount. For instance, it will never be possible to buy enough discount points to reduce the interest rate to 0 percent.

The amount of change in interest rates is often expressed in terms of basis points. A basis point is equal to one-hundredth of 1 percent. Therefore, a reduction in mortgage interest rates of 0.25 percent (25/100 of 1 percent) is a reduction of 25 basis points.

 For Example Lenders offer loans at different interest rates based on charges of a certain number of discount points: 6 percent loan with no discount points 5.75 percent loan with 1.5 discount points 5.5 percent loan with 3 discount points A reduction of the interest rate on a \$150,000 loan from 6 percent to 5 percent for the entire loan term would require a buydown of about \$9,000 (6 percent of \$150,000). This 1 percent prepayment of interest would net the borrower about \$1,128 per year (or about \$94 a month) in reduced mortgage payments.  It would take eight years, the average length of time a person holds a loan, before the borrower’s savings under the mortgage payments would total about \$9,020, the amount paid for the buydown. If he does not keep the loan that long, the permanent buydown was not a good choice.

A temporary buydown, usually paid for by a person other than the buyer, reduces the monthly payments considerably for a short period of time (e.g., one, two or three years). At the end of this period, the borrower’s payment will be the amount computed without the buydown.

The following are some examples of temporary buydowns:

• A 2/1 buydown determines a payment using an interest rate of:
• 2 percent less than the stated note rate the first year;
• 1 percent less the second year; and
• the fixed rate starting the third year.
•    A 3/2/1 buydown uses rates that are:
• 3 percent less than the note rate the first year;
• 2 percent less the second year; and
• 1 percent less the third.
 For Example In a 3/2/1 buydown, the 3% reduction on a \$150,000 loan with an interest rate of 6% would reduce monthly payments by \$267 the first year.If the buyer remains in the property no more than eight years, his total interest reduction would be greater than it would be under the permanent buydown.

The cost of a buydown is equal to the difference between the monthly payments with the buydown and those without the buydown.

 For ExampleA 30-year \$200,000 loan with a 6.5% interest rate has a monthly payment of \$1,264.14. With a 1/1 buydown, the interest rate used to compute the payments would be 1% lower (5.5%) for each of the first two years. The borrower would make a monthly payment of \$1,135.57. Therefore, the cost of the buydown would be: \$1,264.14 – \$1,135.57 = \$128.57 per month x 24 months = \$3,085.68.

## What is an Interest in Residential Mortgage

The interest rate for a loan is not the annual percentage rate. The interest rate is the rate at which the loan amount produces the monthly loan payment. An annual percentage rate (APR), a term established by the Truth in Lending Act, is the rate at which the amount financed (i.e., the loan amount less the prepaid finance costs) produces the monthly loan payment.

The amount of a loan payment that is interest and the amount that is principal can be determined from the monthly payment. The interest can be directly calculated based on the unpaid loan balance as of the last payment. The principal can be determined by deducting the interest from the total loan payment.

For most real estate loans, the interest charged is simple interest. Therefore, if a person owes \$10,000, he would be charged interest on the \$10,000. If he pays \$1,000 of principal to reduce the principal balance to \$9,000, his next interest charge will be based on the remaining \$9,000.

The formula for interest is: Annual Interest = Percent Interest x Loan Balance

The phrase “6 percent interest” translates to: Annual Interest = 6% x Loan Balance.

To get the annual interest amount, multiply the loan balance by the interest rate.

To determine the interest for a period of time other than one year, first calculate the annual interest and then convert the answer accordingly.

 For Example If a lender charged 6% on a \$100,000 loan secured by a home purchased for \$120,000: Annual Interest = 6% x \$100,000 = \$6,000 Monthly Interest = \$6,000 ÷ 12 = \$500 Daily Interest = \$6,000 ÷ 365 = \$16.44

## What Is a Principal Reduction (Equity Growth)

When a monthly payment includes principal and interest, there is no formula to calculate the portion paid to principal directly. This can be determined, however, by calculating and deducting the interest portion of the payment from the total payment.

To calculate the amount of the monthly payment that would go toward principal, take the following steps:

1. Loan Balance x Annual Interest Rate = Annual Interest
2. Annual Interest ÷ 12 = Monthly Interest
3. Monthly Payment – Monthly Interest = Principal Paid that Month
4. Loan Balance – Principal Paid = Remaining Loan Balance
 For Example The loan inception date is February 1. The first payment is due March 1. The interest portion of that payment is charged for the principal outstanding as of February 1 for the use of the funds during February.The loan is a 30-year loan at 10% interest and had an original loan balance on February 1 of \$400,000. The monthly payment due March 1 is \$3,510.29.The interest portion of that is 1/12 of 10% of \$400,000.\$400,000 x 10% = \$40,000 \$40,000 ÷12 = \$3,333.33The \$176.96 difference between the \$3,510.29 payment and the \$3,333.33 interest is the amount by which the loan balance will be reduced. The amount of principal outstanding on March 1 will be: \$400,000 – \$176.96 = \$399,823.04 The next payment, due April 1, will include interest of 1/12 of 10% of \$399,823.04. 10% x \$399,823.04 = \$39,982.30 \$39,982.30 ÷12 = \$3,331.86 The principal portion of the payment will be: \$3,510.29 – \$3,331.86 = \$178.43

With each payment, the principal balance is reduced, so the amount of interest included in the next payment is reduced. The amount of principal in that payment will increase by the same amount the interest is reduced.

In the example above, the interest was reduced from \$3,333.33 to \$3,331.86, for a total reduction of \$1.47. At the same time, the principal portion of the payment increased from \$176.96 to \$178.43, for a total increase of \$1.47. As long as the monthly payments exceed the amount of interest due for the month, they will reduce the debt and result in each payment allocating less for interest and more for the principal amount.

This continues until the entire principal balance is paid in full. In the early years of this type of loan, most of the periodic payment consists of interest. However, in later years, most of the installment consists of principal repayment because there is not much principal left on which to accrue interest from month to month.