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APR Annual Percentage Rate

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

- 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.

- 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.

- PV = 196,000
- FV = 0
- PMT = -1,199.10
- I/Y = ? 6.18948% APR
- N = 30x12 = 360
- P/Y = 12

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

- 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.

- 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

- 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.

- 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.

- 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.