Question

As an economist working for the Minnesota Department of Natural Resources, you project the state will collect $1.7 million every year in revenue from cross-country ski passes. All ski pass revenue collected during the year is deposited in an account that earns 7.5 percent nominal return per year. Assuming inflation is projected at 3.3 percent per year over the next 15 years:

A. What is the nominal value of the account after 15 years of collecting ski pass revenue (each year, you collect $1.7 million)? Assume the first deposit of ski pass revenue will be made into this account in one year. (4 pts)

B. What is the real (inflation adjusted) interest rate earned on this account? Note: looking for a rate, not a value the ski pass revenue in the account.

Answer 1

A)

Here they are depositing 1.7 million every year and we have to calculate amount that is there after n years.

In such a case formula is given by:

FV = (P/i)((1 + r)ⁿ - 1)

When we have to calculate nominal return i = nominal interest rate = 7.5% = 0.075

P = Periodic Payment = 1.7 million

n = time = 15

We have to calculate FV

=> FV = (1.7 million/0.075)((1 + 0.075)¹⁵ - 1) = 44401220

Hence Nominal value of the account = $44401220

B)

Here they are depositing 1.7 million every year and we have to calculate amount that is there after n years.

In such a case formula is given by:

FV = (P/i)((1 + r)ⁿ - 1)

When we have to calculate nominal return i = real interest rate = nominal interest rate - expected inflation rate = 7.5% - 3.3% = 3.2% = 0.032

P = Periodic Payment = 1.7 million

n = time = 15

We have to calculate FV

=> FV = (1.7 million/0.032)((1 + 0.032)¹⁵ - 1) = 32085752.9

Hence Nominal value of the account = 32085752.9

the real (inflation adjusted) interest rate earned on this account = $32085752.9