Question

What interest rate is implicit in a $1,000 par value zero-coupon bond that matures in 9 years if the current price is $560.

Answer 1

Solution:

The interest rate implicit rate in a zero coupon bond can be calculated using the following formula

Interest rate = r = (Face value / Current Price)^{(1/ Years to maturity )} - 1

As per the Information given in the question we have

Face value of the bond = $ 1000

Current price of the bond = $ 560

Years to maturity = 9 years

Applying the above values in the formula we have

= ( 1000 / 560 ) ^{( 1/ 9)} – 1

= ( 1.785714 ) ^{( 0.111111 )} – 1

= 1.066545 – 1

= 0.066545

= 6.6545 %

= 6.65 % ( when rounded off to two decimal places )

Thus the Interest rate Implicit in the zero coupon bond = 6.65 %

                                                                                                                                            

Note : ( 1.785714 ) ^{( 0.111111 )} = 1.066545 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.785714,0.111111)