Question

Hy Marks buys a one-year government bond on January 1, 2015 for $500. He receives principal plus interest totaling $527.5 on January 1, 2016. Suppose that the CPI is 200 on January 1, 2015, and 205.0 on January 1, 2016. This increase in prices is different than Hy had anticipated his guess was that the CPI would be at 201.0 by the beginning of 2016.

The nominal interest rate is 5.5%. (Round your answer in percentage points to one decimal place.) The actual inflation rate is 2.5%. (Round your answer in percentage points to one decimal place ) The real interest rate is 3.0%. (Round your answer in percentage points to one decimal place.) Hy's expected inflation rate was 0.5%. (Round your answer in percentage points to one decimal place.) Hy's expected real interest rate was 5.0%. (Round your answer in percentage points to one decimal place '

Answer 1

The total interest received by Hy Marks in one year from 1 January, 2015 to 1 January 2016 is $(527.5 - 500) = $27.5. So nominal interest in this 1 year period will be (27.5*100)/500 = 5.5%. We have got this by applying I=PRT/100, Here I=$27.5, P=$500, R=?, T=1. So we have got nominal interest rate is = 5.5%.

Now inflation rate will be calculated by {(CPI in 2016 - CPI in 2015) / CPI in 2015} *100= {(205 -200)/200}*100 =2.5%. So actual inflation rate is 2.5%. So Real interest rate is Nominal interest rate - Actual inflation rate = 5.5% - 2.5% =3%.

Hy Marks expected price level will just rise to 201 in 2016 from 200 in 2015. So the expected inflation rate was = {(201-200)/200}*100 = 0.5%

As expected inflation rate was 0.5% so expected real interest rate was = 5.5% - 0.5% = 5%. So Hy's expected real interest rate was 5%.