suppose you currently have a mortgage with 10 years remaining with annual paymen
ID: 2709205 • Letter: S
Question
suppose you currently have a mortgage with 10 years remaining with annual payments (the next one coming in exactly one year) at a rate of 6%. The original mortgage amount was a 20-year mortgage for $1 million
a) what is your current annual payment?
b) What is your current mortgage balance outstanding?
c) Assume you are considering refinancing this mortgage with a new 10-year mortgage at the current rate of 4%. What is the present value of refinancing assuming you make all the remaining payments?
Explanation / Answer
Original Amount $1,000,000
Tenure remaining 10 years
rate =0.06
lets find the amount paid for the first 10 years
A= $1,000,000(1+0.06)10 = $179,0848
Amount-Principal = Interest hence $179,0848-$1,000,000=$790847.7 has been paid as interest and principal amount of $1,000,000 is yet to be recovered.
a)current annual payment
A=$1,000,000(1+0.06)11 =$189,8299
therefore current annual payment =A of 11th year -A of 10 year=$189,8299 -$179,0848=$107,450.6
b)current mortgage balance outstanding
assuming we have paid till the 11th year therefore mortgage balance oustanding will be for remaining 9 years
A=$1,000,000(1+0.06)20=$3207135
Therefore deducting amount of 11th year from 20th year wil give remaining mortgage amount $3207135 -$189,8299 =$1308836
c) refinancing this mortgage with a new 10-year mortgage at the current rate of 4%.
Current principal after 10 years $179,0848 rate=0.04,t= 10 years
PV=$179,0848/(1.04)10=$120,9833
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