# APR Annual Percentage Rate - PowerPoint PPT Presentation

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APR Annual Percentage Rate. APR is the true or effective interest rate for a loan. It is the actual yield to the lender. The APR is calculated using the stated interest rate, any prepaid interest (points) or other lender fees. Points.

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APR Annual Percentage Rate

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### APR Annual Percentage Rate

• APR is the true or effective interest rate for a loan. It is the actual yield to the lender.

• The APR is calculated using the stated interest rate, any prepaid interest (points) or other lender fees.

### Points

• Points are loan fees that are viewed as prepaid interest and raise the APR of the loan. One point is 1% of the loan amount.

### Calculation of APR with Points

• Your are purchasing a residence that has a purchase price of \$250,000. You plan on making a down payment of 20%. Your mortgage lender has agreed to finance the loan at 6% for 30 years, monthly payments, and wants 2 points.

### Calculate the monthly payment on the loan amount after making the down payment of \$50,000.

• PV = 200,000

• FV = 0

• PMT = ? -1,199.10

• I/Y = 6.0

• N = 30x12 = 360

• P/Y = 12

The amount of the points that is being required is \$200,000 x 0.02 = \$4,000.

Therefore the amount of the funded loan is \$200,000 less the \$4,000 = \$196,000.

### Calculate the APR (I/Y) based on the calculated payment and a funded loan amount of \$196,000.

• PV = 196,000

• FV = 0

• PMT = -1,199.10

• I/Y = ? 6.18948% APR

• N = 30x12 = 360

• P/Y = 12

### REFINANCE ANALYSIS

• THE PROPER PERSPECTIVE FOR REFINANCING IS TO WEIGH THE DISCOUNTED CASH FLOW SAVINGS OF THE NEW, LOWER PAYMENT AGAINST THE COST OF THE TRANSACTION

### EXAMPLE PROBLEM FROM TEXTBOOK

• ORIGINAL LOAN\$200,000 AT 9% FOR 30 YEARS WITH MONTHLY PAYMENTS

• CALCULATE MONTHLY PAYMENTS PV=200,000 FV=0 I/Y=9.0 N=360 P/Y=12

• PMT= -\$1,609.25

• REFINANCE THE BALANCE AFTER 5 YEARS AT 8% WITH 2 POINTS AND \$1,000 IN OTHER LOAN FEES FOR 25 YEARS WITH MONTHLY PAYMENTS. THE LENDER WILL FINANCE THE COST OF THE POINTS AND FEES.

• WHAT IS THE PAYOFF AMOUNT FOR THE ORIGINAL LOAN?USING THE AMORTIZATION FUNCTION THE PRINCIPAL BALANCE FOLLOWING THE 60TH PAYMENT IS \$191,760.27 WHICH IS ≈\$191,760

• AMOUNT OF THE POINTS:191,760 + 1,000 = 192,760 *0.02 = \$3,855

• AMOUNT OF NEW LOAN = \$191,760 1,000 3,855TOTAL OF NEW LOAN = \$196,615

• CALCULATE THE MONTHLY PAYMENT FOR THE NEW LOAN

PV=196,615 FV=0 I/Y=8.0 N=300

P/Y=12

• PMT = -\$1,517.50

• SINCE THE NEW LOAN IS PAID OFF AT THE SAME TIME AS THE ORIGINAL LOAN, THE FACT THAT THE NEW MONTHLY PAYMENT IS LESS MEANS THE REFINANCE WOULD BE PROFITABLE.

### CALCULATE THE PRESENT VALUE OF THE SAVINGS FROM REFINANCING

• ORIGINAL PAYMENT= \$1,609.25

• NEW PAYMENT= \$1,517.50 91.75

• FV=0 PMT=91.90 I/Y=8.0 N=300 P/Y=12

• PV= -\$11,887.54

### BUT, WHAT IF THE NEW LOAN IS FOR A TERM THAT EXTENDS THE ORIGINAL TERM OF THE LOAN?

• IF THE NEW LOAN IS FOR 30 YEARS AT 8.0% WITH 2 POINTS THE NEW LOAN WOULD EXTEND THE PAYOFF DATE BY 5 YEARS.

• THE MONTHLY PAYMENT WOULD BE

PV=196,615 FV=0 I/Y=8.0 N=360

P/Y=12

• PMT = -\$1,442.69

• THE NEW LOAN WOULD REDUCED THE PAYMENT BY \$166.56 PER MONTH FROM THE ORIGINAL LOAN OVER 25 YEARS OR 300 PAYMENTS.

• HOWEVER, THERE WOULD BE AN ADDITIONAL 5 YEARS OR 60 PAYMENTS IN THE AMOUNT OF \$1,442.69.

### TO EVALUATE THE REFINANCE IN THIS SITUATION, WE NEED TO USE DISCOUNTING.

• FOR PAYMENTS 1 – 300 (25 YEARS)

• FV=0 PMT=166.56 I/Y=8.0 N=300 P/Y=12

• PV= -\$21,580.27

• THIS REPRESENTS THE PRESENT VALUE OF THE SAVINGS OVER THE 25 YEARS

• NEXT WE NEED TO CALCULATE THE PRESENT VALUE OF THE ADDITIONAL PAYMENTS.

• FOR PAYMENTS 301 – 360 (5 YEARS)

• FV=0 PMT= -1,442.69 I/Y=8.0 N=60 P/Y=12

• PV= \$71,151.21

• THIS REPRESENTS THE PRESENT VALUE OF THE ADDITIONAL PAYMENTS BACK TO YEAR 25.

• NEXT WE NEED TO DISCOUNT THIS AMOUNT (\$71,151.21) TO THE PRESENT.

• FV= -71,151.21 PMT=0 I/Y=8.0 N=300 P/Y=12

• PV= \$9,693.39

• THE PRESENT VALUE (BACK TO YEAR 0) OF THE ADDITIONAL PAYMENTS IS \$9,693.39.

### SO, WHAT IS THE NET RESULT?

• LETS EXPRESS THE PV IN TERMS WHERE A SAVINGS IS POSITIVE AND AN ADDITIONAL COST IS NEGATIVE.

• PV OF SAVINGS FOR 25 YEARS =\$21,580.27

• PV OF ADDITIONAL PAYMENTS FOR 5 YEARS = -\$9,693.39

• THEREFORE, THE NET RESULT IS A BENEFIT FROM REFINANCING OF \$11,886.88

• WHICH MEANS THE REFINANCING SHOULD BE DONE.