Question

You just obtained a $325,000 adjustable rate mortgage (ARM) with 30 year amortization and a 3 year reset period. Your starting interest rate for the loan is 3% and you believe that your rate in 3 years will rise to 3.75%. If you are correct, what will be your new mortgage payment at the start of the 4th year (i.e., right after the reset period)?

a. $1,407.96

b. $1,493.53

c. $1,281.75

d. $1,370.21

Answer 1

PV of Loan =325000
Number of months =30*12 =360
Rate per month =3%/12 =0.25%
Number of Months =3*12 =36
Monthly Payment =PV/((1-(1+r)^-n)/r) =325000/((1-(1+0.25%)^-360)/0.25%) =1370.2131
Loan Balance at the end of 36 months =PV*(1+r)^n-PMT*((1+r)^n-1)/r)
=325000*(1+0.25%)^36-1370.2131*((1+0.25%)^36-1)/0.25%) =304108.5207

New Rate per month =3.75%/12
Number of months =324
Monthly Payment =Loan Balance at the end of 36 months/((1-(1+r)^-n)/r) =304108.5207/((1-(1+3.75%/12)^-324)/(3.75%/12)) =1493.53(Option b is correct option)