4) Which $1000 bond has the higher yield to maturity, a 20-year bond selling for $800 with a current yield of 15% or a 1-year bond selling for $800 with a current yield of 5%?  5) Consider a coupon bond that has a $1000 par value and a coupon rate of 10%

Computation of Yield to Maturity:

Yield to Maturity = (((Coupon*Years)+Capital Gain)/Years)/Current Price:

For 20 year Bond:

Yield to Maturity = (((1000*15%*20)+(1000-800))/20)/800 = 0.20

For 1 year Bond:

Yield to Maturity = (((1000*5%*1)+(1000-800))/1)/800 = 0.3125

As we can see, 1 year bond has higher yield to maturity.

Computation of Yield to Maturity using rate Function in Excel:

=rate(nper,pmt,-pv,fv)

Here,

Rate = Yield to Maturity = ?

Nper = 2 years 

PMT = $1000*10% = $100

PV = $1,044.89

FV = $1,000

Substituting the values in formula:

=rate(2,100,-1044.89,1000)

rate or Yield to Maturity = 7.50%