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.
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)
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
Consider a 30-year, $115,000 fixed-rate mortgage with a nominal annual rate of 5.65 percent
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