Question

If expected inflation is 5% per annum and a typical burger costs $10 today, how much will a
typical burger cost in 5 years from now in nominal terms?

Answer 1

The expected rate of inflation is 5% per annum or per year. Let us denote the inflation with π. Hence

π = 0.05

A typical burger costs $10 today. Let us denote this as P. Hence

P=$10

Now, if the inflation rate is π, then after one year, the increase in the price of that typical burger would be

∆P = π.P

Hence, after one year, price of the burger will be

P1 = P+∆P = P+π.P

or, P1 = P(1+π).......(1)

Now, again after 2 years, the price P1 will rise again. Hence,

∆P1 = π.P1

After 2 years, price of the burger will be

P2 = P1+∆P1 = P1(1+π)

or, P2 = P(1+π).(1+π)

or, .......(2)

Similarly, after 5 years from now or at the 4th year in future, the price of the burger will be

........(3)

It is given that, P=$10 and π=0.05

Hence,

or, P4 = $12.1 ~ $12

Hence, after 5 years from now, the burger will cost $12 in nominal terms.

Hope the solution is clear to you my friend.