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%