Question

1.  A First State Bank savings account pays interest semi-annually with an effective annual rate of 4.4%. What is the stated or nominal interest rate the bank is offering?

2. An 8-year semi-annual payment coupon bond, $1,000 face, has an expected return of 4% and a coupon of 6%. What is the bond’s current yield?

3. You purchase a 4-year, 4% coupon bond for par. Interest is paid annually. One year later, you sell the bond for $1,100. What is your interest yield, capital gains yield and total yield on this bond?

Answer 1

1. EAR =4.4%
(1+Nominal Rate/2)^2-1 =EAR
Nominal Rate =((1+EAR)^(1/2)-1)*2 =((1+4.4%)^(1/2)-1)*2=4.35%

2. Par Value =1000
Semi annual Coupon =6%*1000/2 =30
Semi annual YTM =4%/2 =2%
Number of Periods =8*2 =16
Price of Bond =PV of Coupons+PV of Par Value =30*((1-(1+2%)^-16)/2%)+1000/(1+2%)^16 =1135.7771
Bond's Current Yield =Annual Coupon/Price of Bond =60/1135.7771 =5.28%

3. Coupon =4%*1000 =40
Interest Yield =Coupon/Price =40/1000 =4%
Gains Yield =(Price on year later-Price today)/Price today =(1100-1000)/1000 =10%
Total Yield =Interest Yield+Gains Yield =4%+10% =14%