Calculate the price of a zero-coupon bond that matures in 13 years if the market
ID: 1176064 • Letter: C
Question
Calculate the price of a zero-coupon bond that matures in 13 years if the market interest rate is 5.55 percent. Assume semiannual compounding
The past five monthly returns for PG&E are ?3.39 percent, 4.43 percent, 3.99 percent, 6.80 percent, and 3.80 percent. Compute the standard deviation of PG&E’s monthly returns. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
What is the future value of a $530 annuity payment over four years if interest rates are 8 percent
Explanation / Answer
1) Price of a zero-coupon bond $ 490.82 Working: Current Price = Face Value x Present Value of 1 = $ 1,000.00 x 0.4908 = $ 490.82 Working: Present Value of 1 = (1+i)^-n Where, = (1+0.02775)^-26 i 5.55%/2 = 0.02775 = 0.4908 n 13*2 = 26 2) Standard deviation of PG&E’s monthly returns 3.43% working: a. Average of five month returns: Month Return(%) 1 -3.39 2 4.43 3 3.99 4 6.80 5 3.80 Total 15.63 Average return is 15.63 / 5 = 3.13 b. Calculation of Variance: Month Return(%) Average return a b c=(a-b)^2 1 -3.39 3.13 42.46 2 4.43 3.13 1.70 3 3.99 3.13 0.75 4 6.80 3.13 13.50 5 3.80 3.13 0.45 Total 58.86 Varaince = 58.86 / 5 = 11.77 c. Calculation of standard deviation: Standard deviation = Variance ^(1/2) = 11.77 ^ (1/2) = 3.43 3) Future value of a $530 annuity payment over four years $ 2,388.24 Working: Future Value of annuity of 1 = (((1+i)^n)-1)/i Where, = (((1+0.08)^4)-1)/0.08 i 8% = 4.506112 n 4 Future Value of annuity = Annuity x Future Value of annuity of 1 = $ 530 x 4.506112 = $ 2,388.24
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