Question

Mr. John made a Price Level Adjusted Mortgage (PLAM) of $100,000 loan for 30 years. Nominal interest rate is equal to 24% and payments are made monthly. The lender and borrower agreed that loan balance will be indexed to the CPI (Consumer Price Index) and adjusted annually. If the CPI is equal to 12% at the end of the first year, what is the value of the each monthly payments during the second year? (Answer is rounded)

1028.61
	2001.60
	1152.05
	2241.80
	2201.77

Answer 1

Solution

Let us find the balance of principal after the 1st Year
B = P[(1 + i)^n - (1 + i)^p]/[(1 + i)^n - 1]
Here P=100,000
n=30*12=360
p=12
i=2% per month (24% pa)
B=100000*[(1.02)^360-1.02^12]/(1.02^360-1)
B=99978.48
So, Principal Balance after the first year =	$                 99,978.48
In the 2nd year, CPI is 10% , so interest rate =24%*1.12
Monthly interest rate=24%*1.1/12
Formula for loan amortization =
A= [i*P*(1+i)^n]/[(1+i)^n-1]
A = periodical installment=??
P=Loan amount =99978.48
i= interest rate per period =(24%*1.12/12)
n=total no of payments=29*12=348
A=24%*1.12/12*[99,978.48*1.022^348]/(1.022^348-1)
A=2241
So the Monthly Installment amount in second year=	$                    2241.80

Option D