Question

Mr. John made a Price Level Adjusted Mortgage (PLAM) of $100,000 loan for 30 years. Nominal interest rate is equal to 12% 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 10% at the end of the first year, what is the value of the each monthly payments during the second year?

Answer 1

Principal Amount = $100,000

Term = 30 years

No of periods = 30 * 12 = 360 months

Nominal Interest rate = 12%

Monthly interest rate =12.68% / 12 = 1%

CPI =10%

Monthly Amount Payment = Principal * (Monthly interest rate / (1 - (1 + Monthly interest rate)^{-no of periods}

Monthly Amount Payment = $100,000 * (1% / (1 - (1 + 1%)^-360

Monthly Amount Payment = $1028.61

Month	Beginning Balance	Monthly Payment	Interest Payment	Principal Payment	Ending Balance
1	$100,000.00	$1,028.61	$1,000.00	$28.61	$99,971.39
2	$99,971.39	$1,028.61	$999.71	$28.90	$99,942.49
3	$99,942.49	$1,028.61	$999.42	$29.19	$99,913.30
4	$99,913.30	$1,028.61	$999.13	$29.48	$99,883.82
5	$99,883.82	$1,028.61	$998.84	$29.77	$99,854.05
6	$99,854.05	$1,028.61	$998.54	$30.07	$99,823.97
7	$99,823.97	$1,028.61	$998.24	$30.37	$99,793.60
8	$99,793.60	$1,028.61	$997.94	$30.68	$99,762.93
9	$99,762.93	$1,028.61	$997.63	$30.98	$99,731.94
10	$99,731.94	$1,028.61	$997.32	$31.29	$99,700.65
11	$99,700.65	$1,028.61	$997.01	$31.61	$99,669.04
12	$99,669.04	$1,028.61	$996.69	$31.92	$99,637.12

The amount of principal remaining after 1 year can be estimated from the above amortization table  

Principal after 1 year = $99,637.12

Principal adjusted for inflation = Principal after 1 year * (1 + CPI)

Principal adjusted for inflation = $99,637.12 * (1 + 10%)

Principal adjusted for inflation = $109,600.83

New Monthly Amount Payment after 1 year = Principal * (Monthly interest rate / (1 - (1 + Monthly interest rate)^{-no of periods}

New Monthly Amount Payment after 1 year = $109,600.83 * (1% / (1 - (1 + 1%)^-348

New Monthly Amount Payment after 1 year = $1,131.47