Constant vs actual dollar; inflation-free rate on loan

Constant dollar and actual dollar

• Actual dollars (current dollars) are the amounts of money actually paid or received at a given date, including the effect of inflation. A bank instalment of Rs 5,500 is an actual-dollar amount.
• Constant dollars (real dollars) are amounts expressed in the purchasing power of a chosen base year (usually today). Actual = constant × (1 + f)^n, where f is the general inflation rate and n the number of periods from the base.

Interest rates: the market (combined) rate i applies to actual dollars; the inflation-free (real) rate i' applies to constant dollars. They are related by i = i' + f + i'f, so i' = (i − f)/(1 + f).

Loan problem (monthly)

Actual-dollar loan: Rs 1,00,000 repaid by 24 payments of Rs 5,500, so the monthly market rate i satisfies

1,00,000 = 5,500 (P/A, i, 24)   →   (P/A, i, 24) = 18.1818

Trial values: i = 2% gives (P/A,2%,24) = 18.9139; i = 3% gives 16.9355. Interpolation: i = 2% + 1% × (18.9139 − 18.1818)/(18.9139 − 16.9355) = 2.37%. Exact solution: i = 2.352% per month (nominal 28.22% per year; effective 32.2% per year).

Inflation-free monthly rate, with f = 0.75% per month:

i' = (i − f)/(1 + f) = (2.352% − 0.75%)/1.0075 = 1.590% per month

Answer: The inflation-free interest rate is about 1.59% per month (about 20.8% effective per year); the market rate on the loan is 2.35% per month.