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Rina8888 [55]
3 years ago
10

Interest rates on 3-year Treasury securities are currently 1.92%, while 10-year Treasury securities yield 5.62%. If the pure exp

ectations theory is correct, what does the market believe that 7-year Treasury securities will be yielding 3 years from now
Business
1 answer:
FromTheMoon [43]3 years ago
3 0

Answer: 7.24%

Explanation:

From the question, we are told that:

3 years treasury securities have an interest rate = 1.92%

10 years treasury security has an interest rate = 5.62%

Let the 7 year treasury security interest in 3 years be represented by z.

Based on the expectation theory

( 1+1.92%)^3 × (1 + z%)^7 = (1 + 5.62%)^10

(1+0.0192)^3 × (1 + z%)^7 = (1 + 0.0562)^10

(1.0192)^3 (1 + z%)^7 = (1.0562)^10

1.05871(1 + z%)^7 = 1.72767

Divide both side by 1.05871

(1 + z%)^7 = 1.72767/1.05871

(1 + z%)^7= 1.6319

1 + z% = 1.6319^1/7

1 + z% = 1.6319^0.1429

1 + z% = 1.0724

z% = 1.0724 - 1

z% = 0.0724

We then convert the decimal to percentage

z = 7.24%

The market believes that 7-year Treasury securities will be yielding 7.24% in 3 years .

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An individual wants to have $95,000 per year to live on when she retires in 30 years. The individual is planning on living for 2
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The amount she would be saving during her working life is  $1,089,64 and the deposit required for each year is $6,624.21

Explanation:

Solution

Given that:

The amount of income needed for retirement income = P×[1-(1÷(1+r)^n)]÷r

Now,

The Interest rate per annum  =6.00%

The Number of years = 2

The Number of compoundings per annum  = 1

The Interest rate per period ( r)=6.00%      

The period per payment (P)=$ 95,000

The Amount required for retirement income = 95000*[1-(1/(1+6%)^95000]/6% =$1,089,643        

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Required deposit for every year (P)=FVA÷([(1+r)^n-1]÷r)

The Interest rate per annum = 10.00%

The Number of years= 30                                          

The number payments per per annum =1                                       The Interest rate per period ( r)=10.00%

The Number of periods (n)=30

Thus,

The Future value of annuity (FVA) = $1,089,643  

Hence the deposit required for each year is = 1089643/(((1+10%)^30-1)/10%)

= $6,624.21

                           

                                                 

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