Question

A reset mortgage allows for one interest rate reset during the life of the loan. The mortgage rate will be reset after 6 years, to fully amortize at the end of the original 30 year period (i.e. after 24 more years). For a 6.625%, $120,000, mortgage, compute the reset payment if the new rate resets to 7.375%. (Hint: calculate how much balance is left after you pay fo r6years at the rate of 6.625%, then use the left balance as the new PV, pay it off for the rest of the 24years @ the rate of 7.375%). Assuming monthly compounding. First six years:

a. 820.719

b. 822.190

c. 824.666

d. 826.147

e. 828.001

Answer 1

Correct Option : a. 820.719

As calculated below.

Step :1	Let us calculate monthly payment
	EMI
	Loan Amount	1,20,000.00
	Interest rate per period =6.625/12	0.552083%
	Number of periods =30*12	360
	EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
	Where,
	EMI= Equal Monthly Payment
	P= Loan Amount
	R= Interest rate per period
	N= Number of periods
	= [ $120000x0.006 x (1+0.006)^360]/[(1+0.006)^360 -1]
	= [ $662.49996( 1.006 )^360] / [(1.006 )^360 -1
	=$768.37
Step 2:	Amount left after 6th year
	Present Value Of Annuity
	c= Cash Flow	768.3731
	i= Interest Rate =6.625%/12	0.5521%
	n= Number Of Periods =24*12	288
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $768.3731[ 1-(1+0.005520833)^-288 /0.005520833]
	= $768.3731[ 1-(1.005520833)^-288 /0.005520833]
	= $768.3731[ (0.7952) ] /0.005520833
	= $1,10,670.88
Step 3	Revise monthly payment
	EMI
	Loan Amount	1,10,670.88
	Interest rate per period =7.375%/12	0.614583%
	Number of periods =24*12	288
	EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
	Where,
	EMI= Equal Monthly Payment
	P= Loan Amount
	R= Interest rate per period
	N= Number of periods
	= [ $110670.88x0.006 x (1+0.006)^288]/[(1+0.006)^288 -1]
	= [ $680.16474644304( 1.006 )^288] / [(1.006 )^288 -1
	=$820.719