精算師SOA歷年真題:November2005ExamFM
發布時間：2014-02-26 共4頁
14. Payments of X are made at the beginning of each year for 20 years. These payments
earn interest at the end of each year at an annual effective rate of 8%. The interest is
immediately reinvested at an annual effective rate of 6%. At the end of 20 years, the
accumulated value of the 20 payments and the reinvested interest is 5600.
Calculate X.
(A) 121.67
(B) 123.56
(C) 125.72
(D) 127.18
(E) 128.50
November 2005 18 Course FM
15. You are given the following term structure of spot interest rates:
Term
(in years)
Spot
interest
rate
1 5.00%
2 5.75%
3 6.25%
4 6.50%
A three-year annuity-immediate will be issued a year from now with annual payments
of 5000.
Using the forward rates, calculate the present value of this annuity a year from now.
(A) 13,094
(B) 13,153
(C) 13,296
(D) 13,321
(E) 13,401
November 2005 19 Course FM
16. Dan purchases a 1000 par value 10-year bond with 9% semiannual coupons for 925. He
is able to reinvest his coupon payments at a nominal rate of 7% convertible semiannually.
Calculate his nominal annual yield rate convertible semiannually over the ten-year
period.
(A) 7.6%
(B) 8.1%
(C) 9.2%
(D) 9.4%
(E) 10.2%
November 2005 20 Course FM
17. Theo sells a stock short with a current price of 25,000 and buys it back for X at the end of
1 year. Governmental regulations require the short seller to deposit margin of 40% at the
time of the short sale. The prevailing interest rate is an 8% annual rate, and Theo earns a
25% yield on the transaction.
Calculate X.
(A) 19,550
(B) 20,750
(C) 22,500
(D) 23,300
(E) 24,500
November 2005 21 Course FM
18. A loan is repaid with level annual payments based on an annual effective
interest rate of 7%.
The 8th payment consists of 789 of interest and 211 of principal.
Calculate the amount of interest paid in the 18th payment.
(A) 415
(B) 444
(C) 556
(D) 585
(E) 612
November 2005 22 Course FM
19. Which of the following statements about zero-coupon bonds are true?
I. Zero-coupon bonds may be created by separating the coupon payments
and redemption values from bonds and selling each of them separately.
II. The yield rates on stripped Treasuries at any point in time provide an
immediate reading of the risk-free yield curve.
III. The interest rates on the risk-free yield curve are called forward rates.
(A) I only
(B) II only
(C) III only
(D) I, II, and III
(E) The correct answer is not given by (A), (B), (C), or (D).
November 2005 23 Course FM
20. The dividends of a common stock are expected to be 1 at the end of each of the next
5 years and 2 for each of the following 5 years. The dividends are expected to grow
at a fixed rate of 2% per year thereafter.
Assume an annual effective interest rate of 6%.
Calculate the price of this stock using the dividend discount model.
(A) 29
(B) 33
(C) 37
(D) 39
(E) 41
November 2005 24 Course FM
21. Which of the following statements about immunization strategies are true?
I. To achieve immunization, the convexity of the assets must
equal the convexity of the liabilities.
II. The full immunization technique is designed to work for any
change in the interest rate.
III. The theory of immunization was developed to protect against
adverse effects created by changes in interest rates.
(A) None
(B) I and II only
(C) I and III only
(D) II and III only
(E) The correct answer is not given by (A), (B), (C), and (D).
November 2005 25 Course FM
22. A 1000 par value bond with coupons at 9% payable semiannually was called for
1100 prior to maturity.
The bond was bought for 918 immediately after a coupon payment and was held to call.
The nominal yield rate convertible semiannually was 10%.
Calculate the number of years the bond was held.
(A) 10
(B) 25
(C) 39
(D) 49
(E) 54
November 2005 26 Course FM
