Given details:
Face Value of a security: $1000.00 ---- Redemeed for face value.
Current Market Price: $577.25 ---- You have just purchased a US treasury bond
Tenure: 5 years ---- Bond will mature 5 years from now
It is a case of calculating zero coupon bond interest because as per given question there will not be any payment until bond matures 5 years from now.
To find rate of interest which can be earned on this bond:
Rate of retunrn on bond ---> (Face Value / Current Market Price of Bond) ^ (1 / Maturity Time) - 1
Put all given figures in this formula
(1000.00 / 577.25) ^ (1 / 5) - 1 -----> 11.62%
Hence answer is option "a" i.e. 11.62%
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