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【2014年度】SOA真题之北美精算师November2005ExamFM②

来源：高顿网校 2014-07-26

　　来到此处收藏北美精算师栏目文章滴孩子们，赶紧来高顿网校北美精算师评论区留言哦。这里有【2014年度】SOA真题之北美精算师November2005ExamFM②
　　7. A bank offers the following choices for certificates of deposit:

　　Term

　　(in years)

　　Nominal annual

　　interest rate

　　convertible quarterly

　　1 4.00%

　　3 5.00%

　　5 5.65%

　　The certificates mature at the end of the term. The bank does NOT permit early

　　withdrawals. During the next 6 years the bank will continue to offer certificates

　　of deposit with the same terms and interest rates.

　　An investor initially deposits 10,000 in the bank and withdraws both principal

　　and interest at the end of 6 years.

　　Calculate the maximum annual effective rate of interest the investor can earn

　　over the 6-year period.

　　(A) 5.09%

　　(B) 5.22%

　　(C) 5.35%

　　(D) 5.48%

　　(E) 5.61%

　　November 2005 11 Course FM

　　8. Matthew makes a series of payments at the beginning of each year for 20 years. The first

　　payment is 100. Each subsequent payment through the tenth year increases by 5% from

　　the previous payment. After the tenth payment, each payment decreases by 5% from the

　　previous payment.

　　Calculate the present value of these payments at the time the first payment is made using

　　an annual effective rate of 7%.

　　(A) 1375

　　(B) 1385

　　(C) 1395

　　(D) 1405

　　(E) 1415

　　November 2005 12 Course FM

　　9. A company deposits 1000 at the beginning of the first year and 150 at the beginning of

　　each subsequent year into perpetuity.

　　In return the company receives payments at the end of each year forever. The first

　　payment is 100. Each subsequent payment increases by 5%.

　　Calculate the company’s yield rate for this transaction.

　　(A) 4.7%

　　(B) 5.7%

　　(C) 6.7%

　　(D) 7.7%

　　(E) 8.7%

　　November 2005 13 Course FM

　　10. A company must pay liabilities of 1000 and 2000 at the end of years 1 and 2,

　　respectively. The only investments available to the company are the following

　　two zero-coupon bonds:

　　Maturity

　　(years)

　　Effective

　　annual yield Par

　　1 10% 1000

　　2 12% 1000

　　Determine the cost to the company today to match its liabilities exactly.

　　(A) 2007

　　(B) 2259

　　(C) 2503

　　(D) 2756

　　(E) 3001

　　November 2005 14 Course FM

　　11. An investor borrows an amount at an annual effective interest rate of 5% and will repay

　　all interest and principal in a lump sum at the end of 10 years. She uses the amount

　　borrowed to purchase a 1000 par value 10-year bond with 8% semiannual coupons

　　bought to yield 6% convertible semiannually. All coupon payments are reinvested at a

　　nominal rate of 4% convertible semiannually.

　　Calculate the net gain to the investor at the end of 10 years after the loan is repaid.

　　(A) 96

　　(B) 101

　　(C) 106

　　(D) 111

　　(E) 116

　　November 2005 15 Course FM

　　12. Megan purchases a perpetuity-immediate for 3250 with annual payments of 130. At the

　　same price and interest rate, Chris purchases an annuity-immediate with 20 annual

　　payments that begin at amount P and increase by 15 each year thereafter.

　　Calculate P.

　　(A) 90

　　(B) 116

　　(C) 131

　　(D) 176

　　(E) 239

　　November 2005 16 Course FM

　　13. For 10,000, Kelly purchases an annuity-immediate that pays 400 quarterly for the next

　　10 years.

　　Calculate the annual nominal interest rate convertible monthly earned by Kelly’s

　　investment.

　　(A) 10.0%

　　(B) 10.3%

　　(C) 10.5%

　　(D) 10.7%

　　(E) 11.0%

　　November 2005 17 Course FM
　　高顿网校之名人哲学：你什么时候放下，什么时候就没有烦恼。

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