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iris [78.8K]
3 years ago
5

If a city of 10,000 experiences 200 births, 60 deaths, 10 immigrants, and 30 emigrants in the course of a year, what is its net

annual percentage growth rate?
Business
1 answer:
kykrilka [37]3 years ago
3 0

Solution:


200 births and 10 immigrants will be added to the population. Total is 210.


60 deaths and 30 emigrants will be taken away from the population. Total here is 90.


Just a reminder that an emigrant is somebody who leaves their own country to lastingly settle into a different country.


Therefore, 210 people are added to the population, and 90 people are to be subtracted, for a net gain of 210 - 90 = 120 people.


What percentage is 120 of 10,000?


<span>120/10,000 = 0.012 = 1.2% annual growth rate</span>

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Both Bond Bill and Bond Ted have 5.8 percent coupons, make semiannual payments,
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a.

Percentage change in Bill Price = (91.8486 - 100) / 100 = -0.0815 or -8.15%

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b.

Percentage change in Bill Price = (109.0298 - 100) / 100 = 0.0903 or 9.03%

Percentage change in Bill Price = (132.0946 - 100) / 100 = 0.3209 or 32.09%

Explanation:

To calculate the percentage change in the price of both the bonds, we assume that the par value of both the bonds is $100 each.

a.

To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

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Total periods (n) - Bill= 5 * 2 = 10

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As the bonds were previously price at par, the YTM or market interest rate would have been same as the coupon rate. Thus, the old market interest rate was 5.8%. Now as the interest rates have risen by 2% new interest rate will be = 5.8 + 2 = 7.8%

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The formula to calculate the price of the bonds today is attached.

Bond Price - Bill = 2.9 * [( 1 - (1+0.039)^-10) / 0.039]  +  100 / (1+0.039)^10

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Bond Price - Ted = $78.1448

Percentage change in Bill Price = (78.1448 - 100) / 100 = -0.2186 or -21.86%

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As the bonds were previously price at par, the YTM or market interest rate would have been same as the coupon rate. Thus, the old market interest rate was 5.8%. Now as the interest rates have fallen by 2% new interest rate will be = 5.8 - 2 = 3.8%

New r or YTM - both Bill and Ted = 3.8% * 6/12 = 1.9% or 0.019

The formula to calculate the price of the bonds today is attached.

Bond Price - Bill = 2.9 * [( 1 - (1+0.019)^-10) / 0.019]  +  100 / (1+0.019)^10

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