Question

Assuming that the current interest rate is 3 percent, compute the present value of a five-year, 5 percent coupon bond with a face value of $1,000. What happens when the interest rate goes to 4 percent? What happens when the interest rate goes to 2 percent?  

Instructions: Enter your responses rounded to the nearest penny (two decimal places).

PV at an interest rate of 3% = $          

PV at an interest rate of 4% = $   

The present value  (Click to select)  falls  rises  when the interest rate rises to 4 percent.

PV at an interest rate of 2% = $

The present value  (Click to select)  rises  falls  when the interest rate falls to 2 percent.

Answer 1

1.When interest rate is 3%:

Information provided:

Face value= future value= $1,000

Yield to maturity= 3%

Time= 5 years

Coupon rate= 5%

Coupon rate= 0.05*1,000= $50

The present value of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

I/Y= 3

N= 5

PMT= 50

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

The value obtained is $1,091.59.

Therefore, the present value of the bond at an interest rate of 3% is $1,091.59.

2.When interest rate rises to 4%:

Information provided:

Face value= future value= $1,000

Yield to maturity= 4%

Time= 5 years

Coupon rate= 5%

Coupon rate= 0.05*1,000= $50

The present value of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

I/Y= 4

N= 5

PMT= 50

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

The value obtained is $1,044.52.

Therefore, the present value of the bond at an interest rate of 4% is $1,044.52.

3.When interest rate falls to 2%:

Information provided:

Face value= future value= $1,000

Yield to maturity= 2%

Time= 5 years

Coupon rate= 5%

Coupon rate= 0.05*1,000= $50

The present value of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

I/Y= 2

N= 5

PMT= 50

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

The value obtained is $1,141.40.

Therefore, the present value of the bond at an interest rate of 4% is $1,141.40.

In case of any query, kindly comment on the solution