1) Consider a Zero Coupon bond that matures in 1 year and has a $1000 face value
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Question
1) Consider a Zero Coupon bond that matures in 1 year and has a $1000 face value. The Bond is currently priced to yield 5%. What is the price you would pay today?
2) Consider a 6% Coupon Bond (Paid Annually) that matures in 1 year and has a $1000 face value. The Bond is currently priced to yield 8% compounded annually. What is the price you would pay today?
3) Consider a 6% Coupon Bond (Paid Semi-Annually) that matures in 1 year and has a $1000 face value. The bond is currently priced to yield 8% compounded semi-annually. What is the price you would pay today?
4) $1000 Face Value 7% Coupon Bond (Paid Semi-Annually) matures in 4 years. If the bond is selling for $1025.46, what is the yield to maturity?
5) $1000 Face Value 7% Coupon Bond (Paid Semi-Annually) matures in 4 years. If the bond is selling for $1000.00, what is the yield to maturity?
Explanation / Answer
1)Given:
Future Value (FV)= $1,000
Interest rate (r)= 5%
Time (t)= 1 year
Formula for computing present value:
PV= FV/(1+r)^t
= $1,000/ (1.05)^1= $952.38
You would pay $952.38 today.
This can also be calculated by using a financial calculator by inputting the below into the calculator:
N=1; FV= $1,000; I/Y=5%
Press the PV button to get the present value amount.
2.Given:
Future Value (FV)= $1,000
Annual payments (PMT)= 0.06*1000= $60
Interest rate= 8%
Time (t)= 1 year
Formula for computing present value:
PV= FV+PMT/(1+r)^t
= $1,000+$60/(1.08)^1= $981.48
This can also be calculated by using a financial calculator by inputting the below into the calculator:
N=1; FV= $1,000; I/Y=8%; PMT= $60
Press the PV button to get the present value amount.
3.Given:
Future Value= $1,000
Annual payments (PMT)= 6%/2= 3%= 0.03*1000= $30
Interest rate= 8%/2= 4%
Time (t)= 1*2= 2
This can be calculated using the time value of money formula:
PV= FV+PMT/(1+r)^t
This can also be calculated by using a financial calculator by inputting the below into the calculator:
N=2; FV= $1,000; I/Y=4%; PMT= $30
Press the PV button to get the present value amount.
PV= $981.14
4.Given:
Future Value= $1,000
Annual payments (PMT)= 7%/2= 3%= 0.035*1000= $35
Present Value= $1,025.46
Time (t)= 4*2= 8 years
This can be calculated using the time value of money formula:
PV= FV+PMT/(1+r)^t
This can be calculated by using a financial calculator by inputting the below into the calculator:
N=8; FV= $1,000; PMT= $35; PV= $1,025.26
Press the I/Y button to get the yield to maturity.
Yield to maturity= 3.135%*2= 6.27%
5.Given:
Future Value= $1,000
Annual payments (PMT)= 7%/2= 3%= 0.035*1000= $35
Time (t)= 4*2= 8 years
Present Value (PV)= $1,000
This can be calculated using the time value of money formula:
PV= FV+PMT/(1+r)^t
This can be calculated by using a financial calculator by inputting the below into the calculator:
N=8; FV= $1,000; PMT= $35; PV= $1,000
Press the I/Y button to get the yield to maturity.
Yield to maturity= 3.35%*2=7%
I hope that was helpful :)
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