Question

Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $900,000 loan at a fixed nominal interest rate of 10% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be (Note: Round the final value of any interest rate used to four decimal places.)
It is likely that you won't like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a 30-year mortgage instead of a 15-year mortgage?
a) $1,521,333.25
b) $1,411,091.71
c) $1,102,415.40
d) $1,300,850.17

Answer 1

Answer and Explanation:

The computation is shown below:

As we know that

Monthly payment of a loan is given by

P =  L [r(1 + r)^n] ÷ [(1 + r)^n - 1]

where,  

P = Monthly payment = ?

r = Interst rate = 0.1 ÷ 12 = 0.00833

n = Term = 15 × 12 = 180

L =  Loan amount = 900000

Now

P = $900,000 [0.00833(1 + 0.00833)^180] ÷ [(1 + 0.00833)^180 - 1]

= $9671.4461

Now

The Monthly payment for 30-year loan

P = $900,000[0.00833(1 + 0.00833)^360] ÷ [(1 + 0.00833)^360 - 1]

= $7898.1441

So,  

Difference is

= $9671.4461 - $7,898.1441

= $1,773.3019

b.

Now

Total payment for 30-year loan is

= $7,898.1441 × 180

= $2,843,331.8871

And,

Total payment for 15-year loan is

= $9,671.4461 × 360

= $1,740,860.2907

So,

Difference is

= $2,843,331.8871 - $1,740,860.2907

= $1,102,471.60

i.e. option c