Question

Question 19 

Consider a 30-year, $115,000 fixed-rate mortgage with a nominal annual rate of 5.65 percent. All payments are made at the end of each month. What is the remaining balance on the mortgage after 5 years? 

Your answer should be between 98,478 and 112,670, rounded to 2 decimal places, with no special characters. 

Answer 1

SOLUTION :

19.

Monthly payments.

Monthly rate, r = 5.65/12 % = 5.65/1200 

=> 1 + r = 1205.65/1200

Number of payments , n = 30*12 = 360 months

PV = mortgage amount = $115000

Let monthly payment be $A

So,

PV = Loan = A((1+r)^n - 1)/(r*(1+r)^n)

=> 115000 = A((1205.65/1200)^360 - 1) / (5.65/1200 *(1205.65/1200)^360)

=> 11500 = A* 173.2394

=> A = 115000 / 173.2394 = 663.82 ($) each month.

FV of payments made for 5 years (n = 60 months)

= A((1+r)^n - 1)/ r

= 663.82((1205.65/1200)^60 - 1) / (5.65/1200)

= 45990.53 ($)

FV of mortgage loan after 5 years

= 115000 * (1 + r)^60 

= 115000 * (1205.65/1200)^60

= 152439.71 ($)

Balance amount still due at the end of 5 years

= 152439.71 - 45990.53

=  106449.18  ($) (ANSWER)

Answer 2

Number of periods =30*12 =360
Rate Per month =5.65%/12
PV =115000
Number of Periods =5*12 =60
The Period monthly payment =PV/((1-(1+r)^-n)/r) =115000/((1-(1+5.65%/12)^-360)/(5.65%/12)) =663.8212
Balance after 5 years =PV*(1+r)^n-PMT*((1+r)^n-1)/r)
=115000*(1+5.65%/12)^60-663.8212*((1+5.65%/12)^60-1)/(5.65%/12))=106539.09