Question

You purchased a bond 10 years ago for $871. Today, the bond pays you $1000. Over the same period, overall inflation is 25%.

The real rate of return on the bond is ________ percent. 2 decimal places answer please. Hint: you need first to convert the bond price to today's dollar.

Answer 1

To calculate the real rate of return, we first need to calculate the nopminal rate of return for the bond.

Let n be the nominal rate of return, so we have:-

871( 1 + i )¹⁰ = 1000

( 1 + i )¹⁰ = 1000 / 871

( 1 + i )¹⁰ = 1.148

# From hit and trial method we can calculate our nominal rate of interest which comes to be as 1.4%

Formula for calculating the real rate of return is:-

r ={ ( 1 + i ) / ( 1 + k ) } - 1

Where i = nominal rate of return = 0.014

k = Inflation = 0.25

= { ( 1 + 0.014 ) / ( 1 + 0.25 ) } - 1

= { ( 1.014 ) / ( 1.25 ) } - 1

= 0.8112 - 1 = -0.18 = -18%

Negative real yields describes when an investment's nominal yield is same or lower than the inflation rate.

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