Question

Suppose you purchase a zero coupon bond with a face value of $1,000, maturing in 21 years, for $212.30. Zero coupon bonds pay the investor the face value on the maturity date. What is the implicit interest in the first year of the bonds life? (Round to the nearest cent).

I got it wrong, so they changed the question a little bit. I reposted it, but it mentions neither of those.

Answer 1

Interest Rate on Zero Coupon Bond = CAGR = [(FV i.e. Face Value/PV i.e. Current Price)^(1/Years to Maturity)]-1

= [(1000/212.3)^(1/21)]-1

= [4.7103^0.0476]-1

= 1.076557-1

= 0.076557

= 7.6557%

Implicit Interest for the First Year = Purchase Price*Interest Rate = 212.3*7.6557% = $16.253 = $16.25