Question

I need some one to do these questions 100%. Please provide me Correct answers in 1-2 hours. I already lost time due to wrong answers.

1.Calculate the present value of a $1,000 zero-coupon bond with 10 years to maturity if the required annual interest rate is 6.5%.

2.A lottery claims its grand prize is $25 million, payable over 25 years at $1,000,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use a discount rate of 7%.

3.Consider a bond with an 8% semiannual coupon and a face value of $1,000. Complete the following table:

Years to Maturity	Discount Rate	Current Price
3	5
3	8
6	8
9	5
9	9

        What relationship do you observe between yield to maturity and the current market value?

Answer 1

1) This is a zero coupon bond. So, PMT = 0.

FV = $1,000

T(Time to Maturity) = 10 years

Annual interest rate (r) = 6.5%

PV = FV/(1+r)^T = 1000/(1.065)¹⁰ = $532.73

Calculation in excel:

Using the PV formula in excel:

So, PV = $532.73

2) This is the case of annuity due becasue the first payment is made immediately.

Periodic payment (PMT) = $1,000,000

Time(T) = 25 years

Discount rate = 7%

PV = ?

PV of annuity due is given by:

Substituing the values,

PV = $12,469,334

This can also be done using a financial calculator using the following inputs:

N = 25; PMT = 1,000,000; FV = 0, I = 7%

Now calculate PV by putting the Pmts in BEGIN Mode.

PV = $12,469,334

3) Because this is a semi-annual coupon bond, Payment willbe made every 6 months.

FV =$1,000

Annual coupon rate = 8%

PMT(Semi-annually) = 8%/2 * FV = $40

Screenshot for formulas:

Here - sign is used in PV because returns negative PV value as it considers PV to be an investment.

Summarized:

Relationship between YTM(Yield to Maturity) and Current Price: