Question

The market price of a semi-annual pay bond is $959.93. It has 12.00 years to maturity and a coupon rate of 6.00%. Par value is $1,000. What is the effective annual yield?

Assume a par value of $1,000. Caspian Sea plans to issue a 5.00 year, semi-annual pay bond that has a coupon rate of 7.82%. If the yield to maturity for the bond is 8.37%, what will the price of the bond be?

Assume a par value of $1,000. Caspian Sea plans to issue a 13.00 year, semi-annual pay bond that has a coupon rate of 5.00%. If the yield to maturity for the bond is 5.0%, what will the price of the bond be?

A bank offers 10.00% on savings accounts. What is the effective annual rate if interest is compounded monthly?

Answer 1

1.Information provided:

Par value= future value= $1,000

Time= 12 years*2= 24 semi-annual period

Coupon rate= 6%/2= 3%

Coupon payment= 0.03*1,000= $30

Current price= present value= $959.93

The question is solved by first calculating the yield to maturity.

Enter the below in a BA Plus II financial calculator to compute the yield to maturity:

FV= 1,000

N= 24

PMT= 30

PV= -59.93

The value obtained is 3.2428.

Therefore, the yield to maturity is 3.2428*2= 6.4857% 6.49%

The effective annual yield is calculated using the below formula:

Effective annual yield= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

Effective annual yield = ( 1 + 0.0649/2)^2 – 1

                                   = 1.0660 – 1

                                   = 0.0660*100

                                   = 6.60%  

2.Information provided:

Par value= future value= $1,000

Coupon rate= 7.82% /2 = 3.91%   

Coupon payment= 0.0391*1,000= $39.10 per semi-annual period

Time= 5 years*2 = 10 semi-annual periods

Market interest rate= 8.37%/2 = 4.1850% per semi-annual period

The price of the bonds is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 39.10

N= 10

I/Y= 4.1850

Press the CPT key and PV to compute the present value.

The value obtained is 977.90.

Therefore, the current price of the bonds is $977.90.

3.Information provided:

Par value= future value= $1,000

Coupon rate= 5% /2 = 2.50%   

Coupon payment= 0.025*1,000= $25 per semi-annual period

Time= 13 years*2 = 26 semi-annual periods

Market interest rate= 5% /2 = 2.50% per semi-annual period

The price of the bonds is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 25

N= 26

I/Y= 2.50

Press the CPT key and PV to compute the present value.

The value obtained is 1,000.

Therefore, the current price of the bonds is $1,000.

4.The effective annual yield is calculated using the below formula:

Effective annual yield= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

Effective annual yield = ( 1 + 0.10/12)^12 – 1

                                   = 1.1047 – 1

                                   = 0.1047*100

                                   = 10.47%

The effective annual yield is calculated using the below formula:

Effective annual yield= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

Effective annual yield = ( 1 + 0.0853/2)^2 – 1

                                          = 1.0871 – 1

                                          = 0.0871*100

                                          = 8.7068%  8.7%.

4.The effective annual yield is calculated using the below formula:

Effective annual yield= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

Effective annual yield = ( 1 + 0.10/12)^12 – 1

                                   = 1.1047 – 1

                                   = 0.1047*100

                                   = 10.47%