What interest rate is implicit in a 1000 par value zerocoupo

What interest rate is implicit in a $1,000 par value zero-coupon bond that matures in 6 years if the current price is $470. Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).

Solution

Current price of the bond = $470

Reedemption value = $1000

Time = 6 Years

So we need to calulate the Interest rate for this zero coupon bon.

So we know that a Zero coupon bond has no coupon and the amount that is received in reedemption is the final payment. So the yeild of a zero coupon bond is such that what we pay today, we gonna get back after 6 years with interest.

Hence the Equation is derived as follows:-

Reedemption value = Current Price * (1+r)^6

Using Financial Calculator

1000 = 470 * (1+r)^6

(1+r) = (1000 / 470 )^1/6

r = 1.134097 - 1

r= 0.134

Using Excel

Excel formula is preetty simple we use Rate function

=rate(no of years, PMT,PV, FV,Ending period, Guess)

=rate(6,0,470,-1000,0,10)

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