Question

5. Robert is getting a mortgage. Which option is a better decision?

Option 1: $100,000 at 6.5% for 30 years, 1% up-front fees of loan amount, monthly compounding.

Option 2: $100,000 at 6.25% for 30 years, no origination fee but a 1.5% discount rates, monthly compounding.

Answer 1

Option 1

Monthly Payment = rP(1+r)^N/[(1+r)^N-1]

For monthly compounding,

r = 0.065/12

N = 30*12 = 360 months

P = 100000

=> Monthly Payment = 100000*( 0.065/12)*(1+ 0.065/12)³⁶⁰/((1+ 0.065/12)³⁶⁰-1) = $632.068

=> Interest Paid = 632.068*360 - 100000 = $127544.48

Option 2

Discount Point Paid = 1.5% of 100000 = $1500

Loan Amount = 100000 - 1500 = $98500

r = 0.0625/12

N = 30*12 = 360 months

P = 98500

=> Monthly Payment = 98500*( 0.0625/12)*(1+ 0.0625/12)³⁶⁰/((1+ 0.0625/12)³⁶⁰-1) = $606.481

Total Amount Paid = Interest + Discount Points = (606.481*360 - 98500) + 1400 = $121233.16

Hence, Option 2 is better option, since the total payment is lower as compared to option 1