Question

Ms. Towne is buying a home for $350,000 and is putting down 20% cash on the purchase. She is financing the rest with a 25 year fixed rate 5.75% mortgage, but is considering a bi-weekly repayment option.

How much interest would the bi-weekly option allow her to save and how long would it take her to pay off the loan with this option?

a) $45,763; 21.8 years

b) $44,330; 21.14 years

c) $49,321; 13.27 years

d) $37,901; 22.23 years

Answer 1

Answer:

Correct answer is:

b) $44,330; 21.14 years

Explanation:

Cost of home = $350,000

Borrowing = 350000 * (1 - 20%) = $280,000

Monthly Interest rate = 5.75% / 12

Tenure = 25 years = 25 * 12 = 300 months

Monthly Payment:

To get monthly payments we will use PMT function of excel:

= PMT (rate, nper, pv, fv, type)

= PMT (5.75%/ 12, 300, -280000, 0, 0)

= $1761.4979

Monthly payment = $1761.4979

Interest payment over life of loan = Monthly payments * Number of months - Loan amount

= 1761.4979 * 300 - 280000

= $248,449

Interest payment over life of loan = $248,449

Now, when biweekly repayment option is considered:

Biweekly payment = 1761.4979 / 2 = $880.7490

Biweekly rate of interest = 5.75% / 26

To get long would it take her to pay off the loan with this option, we will use NPER function of excel:

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

= NPER (5.75%/26, 880.7490, -280000, 0, 0)

= 549.6675 biweekly periods

In number of years = 549.6675 / 26 = 21.14 years

Interest payment over life of loan = 549.6675 * 880.7490 - 280000 = $204,119

Interest amount that the bi-weekly option would allow her to save = $248,449 - $204,119 = $44,330

Interest amount that the bi-weekly option would allow her to save = $44,330

As such option B is correct and other options A, C and D are incorrect.