Question

You plan to buy a $240000 home with a 10% down payment. The bank you want to finance the purchase suggests two options (use semiannual compounding): Option 1: 20-year mortgage at 8.19% APR Option 2: 30-year mortgage at 11.23% APR. What is the equivalent monthly interest rate for each option? Equivalent monthly interest rate Option 1: Equivalent monthly interest rate Option 2: What is the monthly payment of each option? Monthly payment Option 1: $ Monthly payment Option 2: $

Answer 1

Equivalent monthly interest rate Option 1 = (1 + 0.0819/2)^(1/6) - 1

Equivalent monthly interest rate Option 1 = 0.006711380677

Equivalent monthly interest rate Option 1 = 0.6711380677%

Equivalent monthly interest rate Option 2 = (1 + 0.1123/2)^(1/6) - 1

Equivalent monthly interest rate Option 2 = 0.009146613713

Equivalent monthly interest rate Option 2 = 0.9146613713%

Loan amount = 240,000 * (1 - 0.1) = $216,000

Option 1

PV = 216,000

r = 0.006711380677

n = 20 * 12 = 240

$PV = \frac{PMT}{ r } * \left [ 1 - \frac{1}{(1+ r )^{ n }} \right ]$

PMT 0.006711380677" (1 + 0.006711380677)240

216, 000 = PMT 0.006711380677 - * 0.7991808063

216,000 = PMT * 119.0784496905

PMT = $1,813.9302330641

Monthly payment Option 1: $1,813.9302330641

Option 1

PV = 216,000

r = 0.009146613713

n = 30 * 12 = 360

$PV = \frac{PMT}{ r } * \left [ 1 - \frac{1}{(1+ r )^{ n }} \right ]$

PMT 0.009146613713" (1 + 0.009146613713) 360

216, 000 = PMT 0.009146613713 - * 0.9622893692

216,000 = PMT * 105.2071727739

PMT = 216,000 105.2071727739

PMT = $2,053.0919547111

Monthly payment Option 2: $2,053.0919547111

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