Question

Calculate the APR for the following loan. : L/V ratio 80%, price of the house $250,000, interest rate 4.5%, monthly payments, term 20 years. Borrower expects to sell his house and move to a new city after 7 years. Origination fees are 2%.please show on calculator. this is all I have

Answer 1

Case 1: Assuming origination fees are not included in the loan
Loan amount=250000*80%=200000

Step 1: Monthly payments
I/Y=4.5%/12
N=12*20
PV=-200000
FV=0
CPT PMT=1265.2988

Step 2: Loan outstanding after 7 years
N=12*7
I/Y=4.5%/12
PV=-200000
PMT=1265.2988
CPT FV=149232.4521

Step 3: APR
N=12*7
PMT=1265.2988
FV=149232.4521
PV=-200000*(1-2%)
CPT I/Y=0.407%

APR=0.407%*12=4.880%

Case 2: Assuming origination fees are included in the loan
Loan amount=250000*80%*(1+2%)=204000

Step 1: Monthly payments
I/Y=4.5%/12
N=12*20
PV=-204000
FV=0
CPT PMT=1290.6047

Step 2: Loan outstanding after 7 years
N=12*7
I/Y=4.5%/12
PV=-204000
PMT=1290.6047
CPT FV=152217.1086

Step 3: APR
N=12*7
PMT=1290.6047
FV=152217.1086
PV=-200000
CPT I/Y=0.406%

APR=0.406%*12=4.873%