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CSS Audit Tax Finance P-II QUESTION #1229
Question 1
A zero-coupon bond sells for \$250. At maturity in 16 years, it will be redeemed for \$1{,}000. What approximate annual rate of growth does this represent?
  • 8 percent✔️
  • 9 percent
  • 12 percent
  • 25 percent
Correct Answer Explanation
Using the future value formula: \(FV = PV \times (1+r)^n\). So \(1000 = 250\times(1+r)^{16}\). \((1+r)^{16} = 4\). \(1+r = 4^{1/16} = 4^{0.0625}\). \(\ln(1+r) = \frac{\ln 4}{16} = \frac{1.386}{16} = 0.0866\). \(1+r = e^{0.0866} \approx 1.0905\). So \(r \approx 9\%\). Wait: \(4^{1/16}\): \(\log(4)/16 = 0.602/16=0.0376\), antilog \(=1.089\), so \(r\approx 9\%\) = option (B). Re-examining: \(4^{0.0625}=1.0905\Rightarrow r\approx9\%\). Answer: option (B) = 9 percent.