COURSE 2 INTEREST THEORY, ECONOMICS, AND FINANCE

[Pages:41]COURSE 2

INTEREST THEORY, ECONOMICS, AND FINANCE

SAMPLE QUESTIONS

Question No. 1 - 13

14 - 26 27 - 33 34 - 46 47 - 50 51 - 55

Subject Area Interest Theory Microeconomics Macroeconomics Finance Interest Theory/Finance Finance/Economics

(13 questions) (13 questions)

(7 questions) (13 questions)

(4 questions) (5 questions)

Interest Theory

1. Jennifer deposits 1000 into a bank account. The bank credits interest at a nominal annual rate of i convertible semi-annually for the first 7 years and a nominal annual rate of 2i convertible quarterly for all years thereafter.

The accumulated amount in the account at the end of 5 years is X. The accumulated amount in the account at the end of 10.5 years is 1980.

Calculate X.

(A) 1200 (B) 1225 (C) 1250 (D) 1275 (E) 1300

2. A deposit of 100 is made into a fund at time t=0. The fund pays interest at a nominal

annual rate of discount d compounded quarterly for the first two years. Beginning at

time

t=2,

interest

is

credited at

a

force

of

interest

* t

'

1. (t%1)

At time t=5, the

accumulated value of the fund is 260.

Calculate d.

(A) 12.7% (B) 12.9% (C) 13.1% (D) 13.3% (E) 13.5%

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3. For an investment account, you are given:

Date Account Value (before deposit or withdrawal Deposit Withdrawal

1/1/96 3/1/96 4/1/96 T/96 1/1/97

100 104

-

-

-

9

99 118 130

17 X

-

-

-

-

The time-weighted yield rate is 13.75% and the dollar-weighted yield rate is 12.81%.

Calculate T.

(A) 5/1 (B) 6/1 (C) 7/1 (D) 8/1 (E) 9/1

4. Mary purchases an increasing annuity-immediate for 50,000 that makes twenty annual payments as follows:

(i) P,2P,..., 10P in years 1 through 10; and (ii) 10(1.05)P, 10(1.052)P,..., 10(1.0510) P in years 11 through 20.

The annual effective interest rate is 7% for the first 10 years and 5% thereafter.

Calculate P.

(A) 564 (B) 574 (C) 584 (D) 594 (E) 604

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5. Brian buys a 10-year decreasing annuity-immediate with annual payments of 10, 9, 8,... 1. On the same date, Jenny buys a perpetuity-immediate with annual payments. For the first 11 years, payments are 1, 2, 3, ... 11. Thereafter, payments remain constant at 11. At an annual effective interest rate of i, both annuities have a present value of X. Calculate X. (A) 26.6 (B) 27.6 (C) 28.6 (D) 29.6 (E) 30.6

6. Bill purchases an annuity at a price of 10,000. The annuity makes payments of 500 at the beginning of every 6 months for 20 years. The payments are reinvested in a fund which earns interest at an annual effective rate i. Interest payments are received every 6 months and reinvested at a nominal rate of 6% convertible semiannually. Bill realizes an overall effective annual yield of 7% on his original investment over the 20-year period. Calculate i. (A) 5.90% (B) 6.05% (C) 6.20% (D) 6.35% (E) 6.50%

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7. Paul lends 8000 to Peter. Peter agrees to pay it back in 10 annual installments at 7% with the first payment due in one year. After making 4 payments, Peter renegotiates to pay off the debt with 4 additional annual payments. The new payments are calculated so that Paul will get a 6.5% annual yield over the entire 8-year period. Determine how much money Peter saved by renegotiating. (A) Less than 550 (B) At least 550, but less than 600 (C) At least 600, but less than 650 (D) At least 650, but less than 700 (E) At least 700

8. Howard wishes to borrow 1000. Lynn offers a loan at a 10.65% annual effective rate in which Howard would repay the loan with eight equal annual payments made at the end of each year by the amortization method. Ann offers a loan in which the principal is to be repaid at the end of eight years. In the meantime, 9% annual effective is to be paid on the loan, and Howard is to accumulate the amount necessary to repay the loan by depositing eight annual payments at the end of each year into a sinking fund. Calculate the interest rate the sinking fund must earn so that Howard is indifferent between the two offers. (A) 5.8% (B) 7.8% (C) 8.3% (D) 10.3% (E) 12.3%

4

9. An n-year 1000 par value bond with 4.20% annual coupons is purchased at a price to yield an annual effective rate of i.

You are given:

i)

If the annual coupon rate had been 5.25% instead of 4.20%, the price of the

bond would have increased by 100.

ii) At the time of purchase, the present value of all the coupon payments is equal

to the present value of the bond's redemption value of 1000.

Calculate i.

(A) 5.0% (B) 5.5% (C) 5.9% (D) 6.3% (E) 6.5%

10. You are given:

i)

a 10-year 8% semiannual coupon bond is purchased at a discount of X.

ii) A 10-year 9% semiannual coupon bond is purchased at a premium of Y.

iii) A 10-year 10% semiannual coupon bond is purchased at a premium of 2X.

iv) All bonds were purchased at the same yield rate and have par values of 1000.

Calculate Y.

(A) X 3

(B) 2X 5

(C) X 2

(D) 2X 3

(E) X

5

11. Bryan buys a 2n-year 1000 par value bond with 7.2% annual coupons at a price of P. The price assumes an annual effective yield of 12%. At the end of n years, the book value of the bond, X, is 45.24 greater than the purchase price, P.

Assume v1n2% < 0.5.

Calculate X.

(A) 645 (B) 652 (C) 659 (D) 666 (E) 675

12. A 30-year bond has 10% annual coupons and a par value of 1000. Coupons can be reinvested at a nominal annual rate of 6% convertible semi-annually. X is the highest price that an investor can pay for the bond and obtain an effective yield of at least 10%.

Calculate X.

(A) 518 (B) 618 (C) 718 (D) 818 (E) 918

13. At time t = 0, Paul deposits P into a fund crediting interest at an effective annual interest rate of 8%. At the end of each year in years 6 through 20, Paul withdraws an amount sufficient to purchase an annuity-due of 100 per month for 10 years at a nominal interest rate of 12% compounded monthly. Immediately after the withdrawal at the end of year 20, the fund value is zero.

Calculate P.

(A) 41,000 (B) 42,000 (C) 43,000 (D) 44,000 (E) 45,000

6

Microeconomics

14. Identify which of the following items is not an example of moral hazard.

(A) A baseball player with a long term contract elects to stop taking extra batting practice.

(B) A student in his graduating year who has secured a good job elects to not study for his last exam.

(C) An insurance company offers a discount to young drivers who do not drive the car after 9:00 p.m.

(D) A person receiving unemployment insurance ceases looking for a job.

15. A horizontal merger can be depicted by the following chart where:

P=

P1

=

Q=

Q1 =

MC =

MC1 =

price before merger price after merger quantity produced before merger quantity produced after merger marginal cost before merger marginal cost after merger

Identify the Social Gain before and after the merger.

Before

After

(A) A + B (B) A + B + C + D (C) A + B + C + D (D) A + B + C + D + E (E) A + B + C + D + E

A + B + C + D A + B A + B + F + G A + B + C + D A + B + C + D + F + G

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