Question

treasury bills are currently paying 6 percent and the inflation rate is 3.1 percent

Answer 1

Approximate real rate	2.90	%
Exact real rate	2.81	%

Calculations:

(1+nominal interest rate) = (1+real interest rate)*(1+rate of inflation)

For approximate rate we can use the formula: nominal rate = real rate + inflation rate

Let us first compute the approximate real rate. So 6% = real rate + 3.1%

Or approximate real rate = 6% - 3.1% = 2.90%

Now let as compute exact real rate using the equation: (1+nominal interest rate) = (1+real interest rate)*(1+rate of inflation)

So (1+6%) = (1+r)*(1+3.1%)

Or 1.06/1.031 = 1+r

Or r = 2.81%

Answer 2

ANSWER 

a.

Approximate real rate

= Treasury rate - Inflation rate

= 6% - 3.1%

= 2.9% (ANSWER).

b.

Exact real rate 

= (1 +Treasury rate) / (1 + inflation rate) - 1

= (1 + 0.06) / (1 + 0.031) - 1

= 0.0281

= 2.81%  (ANSWER).