7. [8 points] You took a one-year loan at a 4% interest rate, expecting that the

Question

7. [8 points] You took a one-year loan at a 4% interest rate, expecting that the annual growth rates of money velocity, money supply and real GDP would be 0%, 1%, and 2%, respectively. At the end of the year, money velocity was indeed the same, but the money supply has increased by 50 basis points more than expected, while the GDP has increased by 75 basis points less than expected. (a) How much was the annual inflation rate that you expected when you took the loan? (b) How much was the actual inflation rate? (c) Who got lucky: you or the lender? (d) How much is the after-tax real interest rate for the lender if the relevant tax rate is 35%?

Explanation / Answer

We know that from equation of MV=PY

% change in Money Supply+% change in Velocity =% change in Price level + % change in GDP

% change in Velocity = 0

% change in Money Supply=% change in Price level + % change in GDP

1% =% change in Priice level + 2%

% change in Price level =-1% hence expected annual inflation rate is -1%

If GDP increased by 75 basis points,less than expected actual GDP is 1.25%

Money Supply is 1.5%

% change in Money Supply=% change in Price level + % change in GDP

1.5% = % change in Price level+1.25%

0.25% = Actual inflation rate

Answer for C)

As actual inflation rate is positive unlike in the expected case borrower is benifited that is lucky

Answer for D)

Real INterets Rate after Tax = (Nominal Interest Rate(1-0.35)-0.25% = 4%*0.65-0.25% =2.35%

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