Please show all work 8. What\'s the present value of a $1,800 annuity payment ov

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Please show all work

8. What's the present value of a $1,800 annuity payment over 7 years and an interest rate of 9 percent?

A. $8,246
B. $12,243
C. $10,440

D. $9,059

11. A treasury bond bought at the beginning of the year for $1,064 pays $48 in interest payments during the year, ending the year valued at $1,095. What was the percent return?

A. 7.42

B. 8.44

C. 4.88

D. 6.86

17. What’s the current yield of a 4.8 percent coupon corporate bond purchased for $100 and three years to maturity quoted at a current market price of $98.24?

A. 4.13 percent

B. 5.44 percent

C. 4.89 percent

D. 5.12 percent

18. What's the future value of $600 deposited for one year earning an interest rate of 8 percent per year?

A. $636
B. $652
C. $664

D. $648

19. If the risk-free rate is 5 percent and the risk premium is 7 percent, what's the required return?

A. 2 percent
B. 12 percent
C. 15 percent

D. –2 percent

Explanation / Answer

8.) Annuity is annual payment per year

Annuity of $1800 mean annual payment of $1800 per year

present value of annuity = P1/(1+r)1 + P2/(1+r)2 + ....................... + Pn-1/(1+r)n-1 + Pn/(1+r)n

where, Pn is payment in year n and r is interest rate

Payment os for 7 years, therefore, n = 7

So payment for every year is $1800 therefore, P1,P2......P7 = $1800

r= 9%

So Present value of annuity = 1800/(1+0.09)1 + 1800/(1+0.09)2 + ...................... + 1800/(1+0.09)6 + 1800/(1+0.09)7

Therefore, Present value of annuity = $9059.32

So the answer is option d i.e. $9059

11.) Price at the beginning of year = $1064

Interest payment = $48

Year end value = $1095

Return = ((Year end price - Beginning price) + Interest)/Beginning Price = ((1095-1064)+48)/1064 = 0.0742 = 7.42%

So the answer is option A. i.e. 7.42%

17.) Face value of bond = $100

Current market price = $98.42

Coupon rate = 4.8% so the coupon payment = 0.048*100 = $4.8

Current market yield is the yield that discount the future payments of bond i.e. annual coupon payments and payment at maturity to its current market value

Present value of a payment = Cash flow/(1+r)n

where r is rate of interest and n is period of cash flow

Price of a bond = C/(1+r)1 + C/(1+r)2 + ..................... + C/(1+r)n + M/(1+r)n

where C is coupon rate, r is current yield, and M is value at maturity

Now putting values,

98.24 = 4.8/(1+r)1 + 4.8/(1+r)2 + 104.8/(1+r)3

We can solve this equation by using hit and trial, by using all of the given options the value that solve this equation is 5.44%

So the answer is option b i.e. 5.44%

18.) Future value = Present value*(1+r)n

where present value is the present value of amount deposited, r is interest rate and n is time period

In this case, Present value = $600, interest rate i.e.r = 8% and n = 1

So future value = 600*(1+0.08)1 = $648

so the answer is option d i.e. $648

19.) risk free rate = 5%

risk premium = 7%

required return = risk free rate + risk premium

So the required return = 5+7 = 12%

Therefore, the answer is option b. i.e. 12%

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