精算師SOA歷年真題:November2005ExamFM
發布時間：2014-02-26 共4頁
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
