Question

Todd has a $100,000 25-year mortgage with a 12% nominal interest rate convertible monthly. The first payment is due one month after the mortgage is taken out. Twelve years after taking out the mortgage (after making his 144th payment), he refinances with a new nominal interest rate of 8%, again convertible monthly. The new mortgage will be paid off on the same date as the original one. Calculate the difference in the monthly mortgage payment after refinancing.

Answer 1

Answer:

The right solution is "$178.86".

Explanation:

The given values are:

Interest rate,

= 10%

New nominal interest rate,

= 8%

Years,

= 24

As per the question,

On the original loan, the annul installments will be:

=  $100000\times 0.01\times 1.01^{\frac{300}{1.01^{300-1}}}$

=  $1053.22$ ($)

As we know,

The remaining 156 instalments are charged throughout the PV after the 144th deposit,

=  $1053.22\times \frac{(1.01^{156-1})}{(0.01\times 1.01^{156}})$

=  $83,017.90$ ($)

On the refinanced loan, the annul installments will be:

=  $83017.90\times 0.01\times \frac{1.01^{300}}{(1.01^{300-1})}$

=  $874.36$ ($)

hence,

After refinancing, the difference in mortgage will be:

=  $Annual \ installment \ on \ original \ loan-Annual \ installment \ on \ refinanced \ loan$

=  $1053.22-874.36$

=  $178.86$ ($)