Business, 11.07.2019 01:00 Laylahlettiere

A10-year us treasury bond with a face value of $10,000 pays a coupon of 5.5% (2.75% of face value every 6 months). the semiannually compound interest rate is 5.2% (a six-month discount rate of 5.2/2 = 2.6%). what is the present value of the bond?

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Answer from: prissydizzybella5

The Present Value of the bond is $10,231.64.

We have

Face Value of the bond $10000

Coupon rate per year 5.5%

Frequency of int payments Semi-Annual (two periods in a year)

Discount rate per year 5.2%

No. of years to maturity 10 years

First we calculate the coupon interest per period

$C = Face Value * \frac{interest rate}{2}$

$C = 10000 * \frac{0.055}{2}$

C = 10000 * 0.0275

C = 275

We can think of a bond as an instrument have types of cash flows.

One is the coupons we receive from a bond, where we receive a fixed amount per period for a stated number of periods.

An instrument that gives a fixed amount per period for a stated number of periods is known as an annuity.

Hence we can treat the coupon from the bonds as an annuity.

The Present Value formula for an annuity is:

$PV_{Coupons} = C\left \{ \frac{1-(1+i)^{-n}}{i} \right\}$

where

C = Coupon per period

i = discount rate per period

n = number of periods

In this question, we'll get 2*10 =20 coupon payments, so the number of periods, n = 20.

The discount rate per period (i) is $\frac{0.052}{2} = 0.026$ or 2.6% per period.

Applying these values to the equation above we can find the PV of Coupons as:

$PV_{Coupons} = 275\left \{ \frac{1-(1+0.026)^{-20}}{0.026} \right\}$

$PV_{Coupons} = 275\left \{ \frac{0.598484331}{0.026} \right\}$

$PV_{Coupons} = 275 * 15.44291035$

$PV_{Coupons} = 4246.800346$

In addition to the coupon, we also get back the bond's face value at the end of the bond's life. We can treat this as a lump-sum amount we will get back at the end of a stated number of periods. We can find the Present Value of the lumpsum as follows:

$PV = \frac{Face Value}{(1+i)^{n}}$

Substituting the values we get,

$PV = \frac{10000}{(1+0.026)^{20}}$

$PV = \frac{10000}{1.670887521}$

$PV_{lump sum} = 5984.843309$

Finally, we compute the Present Value of the bond as follows:

$PV_{bond} = PV_{Coupons} + PV_{lump sum}$

$PV_{bond} = 4246.800346 + 5984.843309$

$PV_{bond} = 10231.64366$

Answer from: Quest

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%

Answer from: Quest

answer; realistic job preview;

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A10-year us treasury bond with a face value of $10,000 pays a coupon of 5.5% (2.75% of face value ev...

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