Finance 3080 Week 4 (Quiz 2)

What if interest is compounded monthly?

(1+.08/12)^12-1=(1.00667)^12-1=.0830 or 8.30%

A Basic Mortgage Example

A mortgage loan is secured by the collateral of some specified real estate property Suppose you have a 30-year, $300,000 mortgage with a contract rate of 5%. What is the monthly payment FORMULA: PMT(1/.005-1/.005(1.005)^360)=PMT (200-33.2064) PMT=300,000/166.7916=1,798.65

Adjustable Rate Mortgages

A popular way to reduce the monthly payment is the Adjustable Rate Mortgage (ARM) The loan may be quoted as a 2/2/5. The first adjustment is capped at 2%, subsequent adjustments are capped at 2%, and the lifetime increase is capped at 5%. A three-year ARM is fixed at the current rate for three years, then may be adjusted. Typically, subsequent adjustments are made each year. When the rate resets, the monthly payment is recalculated over the remaining term of the mortgage using the new rate ARMs carry lower rates, but expose the borrower to refinancing risk at the end of the fixed period. The shorter the fixed period, the lower the rate. The rate change is usually limited to about 2% per year.

Suppose you have a credit card that charges 1.65% per month (this is pretty typical). What is the APR? What is the EAR?

APR=.0165(12)=.1980 or 19.80% EAR=(1+.0165)^12-1=.2170 or 21.70%

Interest Only Loans

An extreme way to reduce the monthly payment is the INTEREST ONLY LOAN. The loan can be structured as a conventional 30-year fixed rate loan, as an ARM, or a balloon loan. Because THE LOAN DOES NOT AMORTIZE AT ALL, THE ENTIRE PRINCIPAL IS DUE AS A BALLOON PAYMENT. Residential balloon loans carry HIGHER rates, because they typicall are taken out by borrowers who are stretched to the maximum. Commercial balloon loans are usually only available to customers with the highest credit rating because of the risk in the loan. In the amortization table, the loan payment was $1,798.65, but the interest only payment would have been $1,500.

Balloon Loans

Another popular way to reduce the monthly payment is the PARTIAL AMORTIZATION or BALLOON LOAN. The loan may be quoted as a 5/15 or 7/30 meaning that the term of the loan is 5 (or 7) years but the payments are calculated as though the term is 15 (or 30) years. Because THE LOANS DOES NOT FULLY AMORTIZE within the shorter time period, THERE IS A LARGE FINAL (OR BALLOON) PAYMENT Balloon loans carry LOWER rates, but expose the borrower to refinancing risk at the end of the loan. Most commerical mortgage loans are loans are balloon loans with the most common term being 10 years with amortization over 20-30 years

Suppose that the STATED (OR NOMINAL) ANNUAL RATE OF INTEREST IS 8% compounded quarterly. What is the EAR?

EAR=(1+r/m)^m-1 =(1+.08/4)^4-1=(1.02)^4-1=.0824 or 8.24%

Federal Housing Administration

Established in 1934 Created the modern structure for home mortgage loans, permitting equal monthly payments over an extended period, up to 30 years Prior to FHA, banks would only loan for 5-15 years

Special Deals: Tax Refund Services Every year you see tax services offering to help you file electronically. In addition, they will give you your refund on the spot. You get your refund as much as 3 weeks earlier than if you mailed it yourself. Assume that you anticipate a refund of about $1,785. All they want in exchange is a fee, say $85. This is basically a short term loan with interest of $85 on a loan of $1,700 for 3 weeks.

First, find the interest rate for the period. r=85/1700=.05 or 5% Next, convert the rate to an EAR EAR=(1+.05)^52/3-1=1.05^17.3333-1=2.3296-1=1.3296=132.96%

Principal, Interest and Amortization

Note that we can break up the 1st monthly payment into 2 pieces INTEREST=(300,000)*(.005)=1500 PRINCIPAL=1,798.65-1500=298.65 After the 1st month, the new mortgage balance is: BALANCE=300,000-298.65=299,701.35

Effective Annual Rate

The Effective Annual Rate (EAR) is the ACTUAL RATE OF INTEREST paid (or received) after accounting for compounding that occurs during the year. If you want to COMPARE TWO RATES over different compounding periods, you need to COMPUTE THE EAR for each and use that for comparison

Annual Percentage Rate (APR)

Truth-in-lending laws require lenders to provide you with the ANNUAL PERCENTAGE RATE (APR) By legal definition, the APR is calculated as THE SIMPLE PERIODIC RATE (IE, MONTHLY, QUARTERLY) TIMES THE NUMBER OF PERIODS IN A YEARE APR is a stated rate, not an effective rate OK to compare APRs if the compounding periods are similar; but EAR is always OK