sample questions fm2

7/28/2019 Sample Questions fm2

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THEORY OF INTEREST - SAMPLE QUESTIONS

1. On July 1, 1984 a person invested 1000 in a fund for which the force of interest at time t is given by

50/)23( tt

+= where t is the number of years since Jan 1, 1984. Determine the accumulated value of the

investment on Jan 1, 1985.

2. A 9% bond with a 1000 par value and coupons payable semi-annually is redeemable at maturity for 1100. Ata purchase price of P, the bond yields a nominal annual interest rate of 8% compounded semi-annually, andthe present value of the redemption amount is 190. Determine P.

3. On Jan 1, John has the following options for repaying the loana) Sixty monthly payments of 100 beginning Feb. 1b) A single payment of 6000 at the end of K monthsInterest is at 12% compounded monthly. The two options have the same present value. Calculate K.

4. A 1000 par value bond with redemption at par has coupons of 12% payable semiannually, and is priced toyield 10% convertible semiannually. The bond has a term of n years. If the term of the bond is doubled, theprice will increase by 50. Calculate the price of the n year bond.

5. An investor purchased a 5 year financial instrument having the following features:- The investor receives payments of 1000 at the end of each year for five years.- These payments earn interest at an effective rate of 4% per year. At the end of the year, this interested isreinvested at the rate of 3% per year.Calculate the purchase price to the investor to yield 4%.

6. A perpetuity pays 1 at the end of every year plus an additional 1 at the end of every second year. Thepresent value of the perpetuity is K. Interest is at 5% annual. Determine K.

7. An investment fund has a value of 1000 at the beginning and the end of the year. A deposit of 200 wasmade at the end of four months. A withdrawal of 300 was made at the end of seven months. Calculate thedollar weighted rate of interest.

8. A 35 year loan is to be repaid in equal annual installments. The amount of interest paid in the 8th paymentis 135. The amount of interest paid in the 22nd payment is 108. Calculate the amount of interest paid in the29th installment.

9. An investment of 700 is to be used to make payments of 10 at the end of the first year, 20 at the end of thesecond year, 30 at the end of the third year and so on, every year for as long as possible. A smaller finalpayment is paid one year after the last regular payment. The fund earns an effective rate of interest of 5%.Calculate the amount of the smaller final payment.


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Answers

1.

[ ] 03.10461000200/750/4exp100050

23exp1000

12/1

045.

1

2/1

===

+=

=

edtt

AV

t

2.

68.1120)1901100(04.

040999.190)(

04099999.1100

)045(.1000/

1100

04.

045.

1901000

=+=+=

===

=

=

=

==

KCi

gKP

CFrg

C

i

r

Kvn

3.

k

va

monthi

600050.4495100

/01.

01.60==

=

Using logs, K=29.01

4.

05.2

05.

)(50

)(

06.

1000

n

n

aigCCP

aigCCP

gr

CF

+=+

+=

==

==

Subtract 1st equation from 2nd )(20050 2nn vv =

Solve the quadratic 5.=nv Using logs, n=14.21

5.

42.4448

18.5412)(5000)04.1(03.4

5

=

=+=

P

ISP

6.

Payments are ,........2,1,2,1,2,1

1025.1)1()1(

05.

2=+=+

=

ijSet

i

Divide payments into,......1,0,1,0,1,0,1,0

......1,1,1,1,1,1,1

756.2911

1025./1/12

05./1/11

=+

==

==

ji

jPerpetuity

iPerpetuity

nd

st


3/3

7.

%9.933.1008

100

)12/5(300)12/8(2001000

100

)1(

100

300

200

1000

12/7

12/4

==+

=+

=

==

=

=

==

tCAI

i

CABI

C

C

BA

t

8.

72)5.1(144)1(

144

25.

)1(108)1)(1(135

)1(

)1(108

)1(135

)1(

7

14

141414

7

14

28

1

==

=

=

+=+=

=

=

=+

vP

P

v

vvvP

vPWant

vP

vP

vPI tnt

9.

10)(10700 Ia=

Using Trial and Error @n=14, value = 664.52@n=15, value=736.80

So there are 14 regular payments and a final payment at 15.

76.73

)(10700 1514

=

+=

R

RvIa

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