Question 2.1 [2 point/ Assume that the central bank sets the current real short-

Question

Question 2.1 [2 point/ Assume that the central bank sets the current real short-run interest rate to R1 -2% and the private sector believes that this short-run real interest rate will prevail in the future as well. According to the expectations hypothesis, what should be the real interest rate in period t on a two-year loan? What should be the interest rate on a five-vear loan? Question 2.2 [3 points/ Assume that the central bank lowers the short-run real interest rate to zero in period t but the private sector expects that in period t+1, the short-run real interest rate will return to 2% and stay at 2% thereafter. According to the expectations hypothesis, what should be the real interest rate in period t on a two-year and a five-year oan Question 2.3 [3 points] Assume that the central bank lowers the short-run real interest rate to zero in period t and the private sector expects that the short-run real interest rate will remain at zero also in periods t+ 1 and t+ 2, after which it will return to 2% and stay at 2% thereafter. According to the expectations hypothesis, what should be the real interest rate in period t on a two-year and a five-year loan?

Explanation / Answer

Soln: 2.1 , Let r be the real interest rate, the interest rate short term = 2%

So, for 2 year loan the real interest rate can be calculated by using the expectation hypothesis

r = 1.02*1.02 -1 = 4.04%

In 5 year loan the real interest rate = (1.02)5 - 1 = 10.41%

2.2

Soln: Now as we see in the first t year rate is 0 and afterwards, the rate = 2% for future as well

So for 2 year loan,a s per the expectation hypothesis

real interest rate , r = (1+0)*(1+0.02) - 1= 2%

For 5 year loan, r = (1.02)^4 - 1= 8.24%

2.3

Soln : Now as per the central bank and private sector the rate will be 0 at t, t+1, t+2. So, we can say that for 2 year loan the interest rate, r = (1+0)(1+0) - 1 = 0%

For 5 year loan the rate = (1+0)(1+0)(1+0)(1+0.02)(1+0.02) - 1 = 4.04%

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