inflation rate vs interest rate on calculating present value of future money

The question has some ambiguity. If you want to calculate something, you need to define what you are interested in. If you want to think in terms of purchasing power, you can use the inflation rate.

However, using inflation would be the wrong answer in the context of finance or project analysis. In the financial context, you are comparing money now versus money in the future. The basis of comparison is an instrument that bridges money from the present to the future, which are debt instruments.

For example, if you are borrowing to finance a project, your profitability depends on the return of the project in nominal terms versus the cost of financing. What the value of the currency does versus a basket of goods during that time does not matter.

The idea of inflation trading off future returns is a beloved concept of conventional economists, but its usefulness is greatly overrated. Since you cannot purchase the CPI basket and store it indefinitely, there is no obvious necessary relationship between inflation rates and the return on investable assets. (People might invoke model relationships, but that puts a lot of faith in the models.)

To me makes more sense to use the real interest rate, that is the nominal interest rate adjusted for inflation. Because you have to use a discount rate to calculate the present value of money, so I suggest you to use the interest rate adjusted for inflation (that is the nominal interest rate minus the inflation rate) and not the inflation rate per se (since it doesn't tell you the return on your project, but tell you only the purchasing power of the money and you don't want to know that but you want to know the real rate of return on your project, i.e. the nominal rate minus the inflation rate). So, using only the inflation rate is not useful. Instead you should use the inflation rate with regard to the nominal interest rate, in a way that you can calculate the real interest rate that you use to calculate the time value of money