Question

You want to pay off your mortgage on something called an accelerated bi-weekly payment plan (your parents told you to do this). You have a mortgage of $530,000 amortized over 28 years at a rate of 3.8 percent APR compounded semi-annually. (Assume 52 weeks a year.)

a. What would the regular bi-weekly payment be?

b. What would the accelerated bi-weekly payment be?

c. How much quicker would you pay off the mortgage payment?

d. How much interest would you save by doing the accelerated bi-weekly payment?

Answer 1

A mortgage of $530,000,
Amortized over 28 years, at a rate of 3.8 percent APR compounded semi-annually. (Assume 52 weeks a year.)

1) regular bi-weekly payment be...
Payments are made once every two weeks. This means that the payment dates will always fall on a different calendar date. However, it also means that we'll be making twenty six total annual payments, or half of the fifty two weeks in the year.
bi-weekly payment = (Monthly Payment*12) /26
= $2569.62 *12/26 (Monthly Payment is calculated in 1st solution)
= $1185.98

2. accelerated bi-weekly payment be...
Payments are made twice a month. They are also known as semi-monthly payments. Generally, these payments are made on the first and fifteenth of every month. Totally number of yearly bank payments to twenty four times a year.
Bi-Weekly Accelerated Payments= Monthly Payment /2
= {[P x R x (1+R)^N]/[(1+R)^N-1]} /2
= {[$530,000 x 0.3167% x (1+0.3167%)^336]/[(1+0.3167%)^336-1]} /2
= {[4856.59] /[1.89]} /2
= $2569.62 /2
= $1284.81

3. Time Duration for quicker payment...
Meanwhile, what we are really doing is adding a 13th payment (26 payment instead of 24 payment into Year) to our annual number of payments, and splitting it up between 26 bi-weekly payments. In this case means that by paying an extra $98.83 ($1284.81 - $1185.98) in every two weeks we will pay off our loan in almost 293 months instead of the current 336 months, and save $48,352.49 in loan interest in that.

4. Interest would you save by doing the accelerated bi-weekly payment...
With the help of amortization schedule,
Total Interest using Monthly Payment = $331,806.20
Total interest using accelerated bi-weekly payments = $283,453.71
Difference = $48352.49 is savings into loan interest process

(Note : If, There is quite smaller difference into figure, its due to Round off problem into calculation )