Question

Assume a zero-coupon bond that sells for $386 will mature in 25
years at $2,100. Use Appendix B for an approximate answer but
calculate your final answer using the formula and financial
calculator methods. **What is the effective yield to
maturity?** (Assume annual compounding. Do not round
intermediate calculations. Enter your answer as a percent rounded
to 2 decimal places.)

Answer #1

**Calculation using formula**

Face value of the zero coupon bond = FV = $ 2,100

Time to maturity = N = 25 years

Price, PV = $ 386

Annual compounding

Let's assume yield to maturity to be y. Then, P = FV / (1 +
y)^{N}

Hence, 386 = 2,100 / (1 + y)^{25}

Or, y = (2,100 / 386)^{1/25} - 1 = 7.01%

**Calculation using financial calculator**

For yield, we will use the RATE function.

Inputs of RATE function:

Period, N = 25

Payment, PMT = 0

PV = -386

FV = 2100

Hence, yield to maturity = RATE(Period, payment, PV, FV) = RATE(25, 0, -386, 2100) = 7.01%

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