You have decided to invest in two bonds. Bond X is an n-year bonod with semiannual coupons, while bond Y is zero-coupon bond, which is re- deemable in 2 years. The desired yield rate is the same for both bonds. You also have the following information: Bond X:
Par value is 1000.
The ratio of the semi-annual bond rate to the desired semi-annual yield rate, that is is r/i 1.03125.
b. The present value of the redemption amount is 381.50.

Bond Y:
Redemption value is the same as that of bond X.
Price to yield is 647.80.

What is the price of bond X?

The price of the bond X is 1055.09.

Explanation:

The price of Bond X can be determined as follows:

Let:

R = Present value of the Redemption amount of X and Y

i = yield of both Bond X  and Bond Y

For Bond X, we have:

381.5 = R / (1+i)n ………………… (1)

For Bond Y, we have:

647.80. = R/(1+i)(n/2) ……………….. (2)

Use equation (2) to divide equation (1), we have:

381.5/647.8 = 1/ (1+i)(n/2)  ……………………….. (3)

0.588916332201297= 1/ (1+i)(n/2)

(1+i)(n/2) = 1 / 0.588916332201297

(1+i)(n/2) = 1.69803407601573

647.80 = R / 1.69803407601573

R = 647.80 * 1.69803407601573 = 1,099.99, or 1,100

Now, also let:

r = coupon rate of Bond X

P= present value of Cash flows of Bond X  

Therefore, we have:

P = 1000 * (r/2) / (1+i)0.5 + 1000*(r/2)/ (1+i)1++1000 * (r/2) /(1+i)n+ 1100/(1+i)n

It can be observed that we have 2n terms indicating present value of 2n semiannual coupon payments and last term is present value of Redemption amount.

Applying GP formula, we have:

P = 1000 *(r/2) * (1- (1+i)-n) / ((1+i)(1/2) -1) + 1100 * (1+i)-n

Looking at equation (3), we it can be observed that we can have:

(1+i)-(n/2) = 381.5/647.8 = 0.588916

Therefore, we have:

(1+i)-n = 0.5889162= 0.346822

By employing the Binomial approximation, we have:

(1+i)(1/2)= 1+i/2+... very small terms = 1 + i/2

This indicates that:

(1+i)(1/2)-1 = i/2

If we substitute this into the price equation, we will have

P = 1000 *(r/2) * (1-0.346822) / ( i/2) + 1100 * 0.346822 = 1000 * (r/i) * 0.653178 + 381.504

Since r/i = 1.03125, we have:

P = 653.178 * 1.03125 + 381.504 = 1055.09

Therefore, the price of the bond X is 1055.09.

explanation:

the contractual interest rate is the interest the borrower must pay and the interest the lender receives, or more simply, it is the interest rate stated on a bond whereas the market interest rate is “the investors demand for loaning funds”. therefore, bonds can either be sold at a premium, face value, or discount.

1   all nations face the problem of scarcity because there are limited resources and unlimited wants. nations do not have enough factors of production to produce everything that their population wants. entrepreneurial resources initiate businesses to make new goods and services; labor resources produce goods and services.

2 there are four factors of production: natural resources, labor resources, capital resources, and entrepreneurial resources. natural resources are raw materials from nature that are used to produce goods. trees, water, and grains are natural resources. some natural resources, such as wheat and cattle, are renewable

3 wants

things that you do not need to have in order to survive, but would like to have

needs

things that you must have in order to survive

goods

physical products

services

tasks that a business perform for customers

resources

items that people can use to make or obtain what they need or want

determine

to settle or decide by choice of alternatives or possiblities

4 i really dont know