G: have an annual coupon rate of 8 percent and a par value of $1,000 and will mature in 20 years. If you require a 7 percent return, what price would you be willing to pay for a Vanguard bond

The price for a vanguard  bond will be $1204.48

Explanation:

We are given the face value of the bond so now we will look for the present value at which the vangaurd bond can be sold for so firstly we are given the bonds face value which is $1000 and an annual coupon rate of 8% plus the mature period of 20 years so we will use this information to find the bonds future value at a coupon rate which is the face value in 20 years time using the formula Fv = Pv (1+i)^n

where Fv is the future face value of the bond

Pv is the present value of the bond which is $1000

i is the coupon rate of 8%

n is the period the bond will mature in

therefore now we substitute the above mentioned values:

Fv = 1000(1+8%)^20

Fv = $4660.957144 this is the future face value of the bond now we will find the present value of the bond using the interest rate of 7% considering the return i want to find the value of the vanguard bond now using the same above formula but finding the present value at 7% per annum:

Pv= Fv/ (1+i)^n

where Fv is the future value above for the bond

Pv is the present value price of the bond which we are looking for

i is the interest rate i require which is 7%

n is the period of 20 years the bond took to mature.

therefore we substitute to the above mentioned formula:

Pv = $4660.957144/(1+7%)^20 then compute on a calculator

Pv = $1204.48 which will be the the price i'm willing to pay for the vanguard bond.

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