Question

Oppenheimer Bank is offering a 30 year mortgage with an APR of 4.78% based on monthly compounding. With this mortgage your monthly payment would be $1,986 every month, you can make half the payment every two weeks (so that you will make 52/2 =26 payment per year). With this plan, how long will it take to pay off the mortgage if the EAR of the loan is unchanged?

The number of payments will be _____, which is approximately ____ years.

Answer 1

Answer:

First let us calculate Loan amount

Given:

Monthly payment = 1986

Number of monthly periods = 30 *12 =360

Monthly Interest rate = 4.78%/12

To get loan amount, we will use PV function of excel:

PV ( rate, nper, pmt, fv, type)

= PV (4.78%/12, 360, -1986, 0, 0)

= $379400.69664

Loan amount = $379,400.70

APR = 4.78% based on monthly compounding

EAR = [1 + (i/n)] ^n -1

EAR = (1 + 4.78%/12) ¹² - 1 = 4.886125%

EAR of the loan is unchanged

Bi-weekly rate = (1 + EAR) ^1/26 -1 = (1 + 4.886125%) ^1/26 - 1 = 0.183649%

Bi-weekly payment = 1986 / 2 = 993

To get number of payments , we will use NPER function of excel:

NPER (rate, pmt, pv, fv, type)

= NPER (  0.183649%, 993, 379400.69664, 0, 0)

= 659.24

Number of payments = 659.24

Approximate years = 659.24 / 26 = 25.36 years