“Allah
says pray to me,I will answer to your prayer.’’
Principles
of Finance: Time value of money
NO
1 Determine the future values utilising a time preference rate of 12%
1)Tk.7,000 invested for five years .
2)Tk.10,000 for 4 years .
3)Tk.20,000 for 8 years. ANS; 12,336.39,15,735.19,49519.26
NO
2 Mr. Jakir deposited tk.70,000 in the Jamuna bank which pays 13% rate of interest on 10 year time deposit
how much the deposit will grow at
the end of ten years. ANS:2,37,619.26
NO
3 You invest a single amount of tk.15,000 for three years at 10%.At the end of
3 years you take proceeds and
invest them for 12 years at 15%.How much
will you have after 15 years ? ANS: 1,06,817.74
NO
4 Find the compound value (future value)
of tk.12,000 for 6 years at 10% interest rate. Interest is paid .
a)
yearly (m=1)
b)
half yearly(m=2)
c)
bi monthly(m=6)
d)
semi annually(m=2) FV=PV(1+i/m)^mn
e)
quarterly (m=4)
f)
monthly (m=12)
g)
weekly(m=52)
h)
daily(m=360)
NO
5 Find the compound interest on tk.15,000 for 3 years if interest is payable
half yearly the rate for the first two years 6% and 3rd year 9%.
ANS: FV=18,436.25 &
INTEREST=3,436.25
NO
6 Agrani bank Ltd. Pays 12% interest on time deposit interest compounded half
yearly. What is the periodical interest rate ? (EIR= I per= I nom / m ) ANS: 6%
NO
7 The city bank Ltd. Pays 7% interest compounded quarterly what is the
effective or equivalent interest rate ? ANS: 7.19% { EIR=(1+ i/m)^m -1}
NO
8 What is the future value of 5 years ordinary annuity that promises to pay
tk.300 each year .ANS:1,725.22
FVA=A/I {(1+i)^n -1}
NO
9 What is the future value of 5 years annuity due that promises to pay tk.300
each year .ANS: 1,845.99
FVA(due)= A/I(1+i){(1+i)^n -1}
NO 10 Find the future value of the following annuities
:
a)
Tk.400 per year for 10 years at 10%
ANS: 6374.97
b) Tk.200 each year for 5 years at 5% ANS: 1105.13
c) Tk.2,000 a year for 7
years at 9% ANS:
18400.87
d)
Tk.4,000 at the beginning of each year for 3 years at 3% ANS: 13240.50
e)
Tk.3,000 at the start of every year for 5 year at 12% ANS: 21345.55
NO 11 Mr. Saroar Hossain wants to invest tk.25,000 tk.40,000
tk.50,000, and tk.60,000 at the beginning of the following 4 years
respectively. If the expected rate of return is 10% what amount he will receive
after 4 years.
ANS:
2,16,342.50
NO 12 What is the present value of tk.12,000 in 2
years at 10% . PV=FV/(1+i)^n
NO 13 What is the present value of 12,000 due in 2
years at 10% compounded interest according as the interest is paid
a)
yearly (m=1)
b)
half yearly(m=2)
c)
bi monthly(m=6)
d)
semi annually(m=2) PV=FV/(1+i/m)^mn
e)
quarterly (m=4)
f)
monthly (m=12)
g)
weekly(m=52)
h)
daily(m=360)
NO 14 Mr. Shah Alam will receive tk.7,500 a year for
next 15 years from City bank it an 9% interest rate is applied what is the
current value of the future payments ? PVA= 60,455.16
NO 15 Calculate the present value of each of the
following cash flows using a discount rate of 12%.
1) Tk.6,000 cash inflow at the end of
each of the next 6 years.
2) Tk.6,000 cash inflow at the
beginning of each of the next 6 years. ANS: 14,668.44 & 27,628.66
EXAM
PROBLEM
NO
15 You have a plan to buy a car after 6 years from now .Then the price of the
car will be tk.4 lacks .You want to
accumulate this money in a bank account
by monthly Installments which gives you
12% interest .What is your
monthly installment. ANS: TK.3,820.07
NO16
Mr. Khan is a senior executive of Glaxo
Ltd. Currently he paid tk.80000 per month as the salary from
Glaxo.
Mr. Khan has a current bank
account at IFIC bank Dilkusha branch which is his salary account and naturally
the salaries are being Deposited
on the last day on the month. He has been advised by the manager of IFIC
bank to open a savings account in
his bank. Finally Mr. Khan is convinced to open a savings account at the
same bank. Mr. Chowdhury who is
the manager Of that branch agreed to arrange a direct debit of 7.5% of his
salary what would be transferred to his savings account on the
last day of the month . The current Interested on
savings account is 13% monthly
compounded. How much Mr. Khan Money
would be growing in 13 years?
ANS:24,20,556.04
NO
17 Mr. Ali opens a DPS account at Sonali bank DU branch on 1st
January 2003 .He Deposits tk.33 at the
beginning every week into his
account .The bank offers 12.5% interest
compound weekly on DPS how much
will Mr. Ali receive on maturity the DPS will matured at on 31,December,2017? ANS:75,770.32
NO
18 Determine the number of years to be required for the initial deposited pf
tk.15,000 to grow at tk.25,000 at
annual rate of 12.50%. ANS :4.34
Years .
NO
19 Inzamam has tk.10,00,000 to make investment . His advisor Mr. Zia has
suggested an investment alternative
that pays on stated rate but will
return tk.18,00,000 at the end of 5 years .What annual rate of return will
Inzamam earn on this investment. ANS:12.47%
NO
20 Your brother committed to present you a personal computer on your
graduation after 5 years from now .The
computer will cost tk.30,000 at
that time .Your brother planning to
accumulate the fund by depositing equal
amount of money in a bank account
bearing 8% interest rate per annum.How much should your brother depoit
in the bank account if the
deposits are made (1) yearly (2) quarterly. ANS: TK.5.113.49 TK.1234.70 .
NO
21 You have applied for a mortgage of tk.60,000 to finance the purchase of a
new car the bank will require you
to make annual payments of
tk.7,074.55 at the end of next 20 years .Determine the interest rate on this
mortgage.
{PVA=A(PVIFAi,n)} ANS: 10%
NO
22 What is the rate of return on an investment of tk.10,6066 if the company
will receive tk.2,000 each year for
the next 10 years. {PVA=A(PVIFAi,n)} ANS: 13.56%
NO
23 Tk.1,000 is to be receive at the end of one years tk.500 at the end of two
years and tk.100 at the end of three
years .What is the aggregate
present value of these receipts assuming a discount rate of 8%. ANS:1,434
NO
24 A person wishes to accumulate tk.8,000 by the end of 5 years by making equal
annual end of year deposits
over the next 5 years .If he
can 7% on his investments how much must he deposit at the end of each year to
meet this goal. ANS: TK.1,391.13 .
NO
25 At the end of three years how much is
an initial tk.1,000 deposit worth assuming a quarterly compounded
annual interest rate is 10%.
ANS: 1,344.89.
NO
26 What is the present value of tk.6,000 to be received at the end of 6 years
if the discount rate is 12% ?
ANS: 3,039.79
NO
27 If you wish to save a portion of the earnings from job this year to make your first tuition payment next
semester a year from now tuition
will be tk.600 and the bank will pay 5 percent interest compounded annually
.How much money must you put in
the bank now in order to have tk.600
next year ? ANS: 571.43
NO
28 What is the present value of the following cash flows at an interest rate of
12% per year?
a)
Tk.100 received 5 years from now.
b)
Tk.100 received each year beginning one year
from now and continuing for ever. {PV(pty)= p/i}
ANS: 56.74 &833.33
NO
29 You have a plan to accumulate
tk.12,00,000 ten years from now for buying a car You are deciding to deposit
a certain amount of money in a special account
that Will provide you 9.5% interest per
annum.
1)
What will be your annul deposit at the beginning
of each year.
2)
What will
be your annual deposit at the end of year?
3)
What will be your half yearly deposit?
ANS: TK.70,428.66 TK.77,119.38 TK.37,260.56
NO 30 Find the future value of the following
investment the interest rate is 8% per year
Compound annually.
1)
TK.100 is invested each year beginning one year
and continuing through year 10 when the proceds are withdrawn.
2)
Tk.100 is invested each year starting today
through year 10 when proceds are withdrawn.
ANS; 1,448.66 & 1,564.55
NO
31 You have tk.50,000 at the end of 10 years. To accumulate this money you have
decide to save a certain
Amount at the end of each of the next
10 years and deposit it in the bank. The bank pays 8% interest compound
Annually for long term deposit . How
much will you have to save each year .
ANS 3,451.47
NO 32 Your father has got an offer from a real
estate company for an apartment at Baridhara costing tk.44 lac. If the
payment of tk.4.65 lac each . The
first installment will be made immediately .
If the bank interest rate is 10%
.You required to suggest your
father as to which offer should be accepted. ANS: PV 43,54,683..
NO
33 The management of a limited company has decided to establish a pension fund
for its employees . So that the 10
Employees can get tk.2,000 per month
as pension for the next 10 years 1st
payment is made now. How much the
company set aside if the fund earns a 9% interest
compounded 12 in a year . Calculate total interest also.
ANS 15,90,673 & 8,09,327.
NO 34 Loan payment determine the equal annual end of
year payment required each year , over the life of the loans
shown in the following table to repay them fully during the stated term
of the loan .
|
Loan
|
Principal
|
Interest
rate
|
Years
|
ANS
|
|
A
B
C
D
|
12,000
60,000
75,000
4,000
|
8%
12%
10%
15%
|
3
10
30
5
|
4,656.38
10,619.47
7,955.87
|
NO 35 What will be the present value of an
annuity of tk.3,000 to be receive for next 5 years if the discounting rate
Is 12%? ANS : 10,814
NO
36 Calculate the terminal value of tk.12,000 deposited in a bank account for next 10 years . The deposit
will be
made in the beginning of the year .
Interest rate is 14%? And what will the terminal value if the deposit are made
at the end of each of the year? ANS:
2,64,534 &2,32,048
NO
37 Suppose that you are planning to deposit tk.16,000 in a bank in the
beginning of every year for next 4 years . It
the bank offers you 10% interest p.a,
how much will be accumulated in your bank account at the end of 4th
year ?
ANS : 81,682
NO
38 Refer to the above problem if you want to accumulate tk.81,682 at the end of
4th year to meet a certain
requirement how much should you
deposit in a bank account for next four years . Assume that the deposit should
be made in the beginning of each
year. ANS: 16,000
NO
39 BTI has been doing estate business for last 10 years you . You have selected an apartment of BTI at
Dhanmondi costing tk.25,00,000 .you have three offers .
a)
Pay full in cash.
b)
Pay 25% of the cost in cash immediately and pay
tk.2,20,000 in each installment for next 10 years .
c)
Pay 40% present of the cost in cash and take a
loan of tk.15,00,000 from Bangladesh hose building finance
corporation at 15% interest to be repaid in equal monthly installment
over next 20 years
.
Which offer should you accept ? Assume 12%
opportunity cost. ANS: 25,00,000
18,68,044 27,93,758
NO
40 Exactly 10 years from now Mr. Rahman will start receiving a pension of
tk.5,000 a year . The payment will
continue for 5 years . How much is
the pension worth now if he expected
rate of return is 12% ?
NO
41 A real estate company by an arrangement with BHBFC granted you tk.3,00,000
as loan at 12% interest rate p. a.
you are to pay ;
a)
In ten annual equal installments.
b)
In twenty half yearly equal installments.
c)
In 120
monthly equal installment.
Calculate the installment money
under the above three methods.
NO
42 A man borrows tk.6,000 at 6% and promises to pay off the loan in 20 annual payments
beginning at
the end of the 1st
year. What is the annual payment necessary?
ANS: A=523.11
NO
43 A man borrows tk.5,000 .He paid it by six equal installments in two years .
The interest rate was 15%
on unpaid balance. Find the amount of each installment. ANS: A=985.09
NO
44 Find the present value of the stream
of cash flows shown in the following table. Among the firms
opportunity cost is 12%. ANS
l:15,376.92
NO
45 In what time will a sum of tk.5,000 will be doubled at 5% compound interest
. ANS: n=14.21
NO
46 The cost of a new machine will be tk.95,000 in future . If tk.5,968 is
retained out profits each year and
deposited into a fund to
accumulate at 5% compound interest then how many years it will take to
create the desired amount. ANS:
n=12
NO
47 In what time will a sum of tk.5,000
will be doubled at 5% compound interest use rule 72.
(Rule 72, n=72/i)
NO
48 In what time will a sum of tk.5,000 will be doubled at 5% compound interest
use rule 69.
(Rule 69, n=0.35+69/i)
NO
49 Taking a loan of 9,000 from a bank a
man was not able to pay it till the end
of 4 years . Then the
bank demanded tk.11,250 from him.
How much percent of interest compounded yearly on the
demanded money he was paid? ANS : i=5.73%
NO
50 Suppose Mr. Ali takes out a tk.5,000 five year loan at 9% . The loan is
payable at 5 annual installments
Prepare the loan amortization
schedule. ANS: A=1,285.46
NO
50 AB limited is creating a sinking fund to redeem its preference capital of
tk.5,00,000 issued on 6 April
1994 and maturing on 5
April 2005
. The first annual payment will be able made on 6
April 1994.
The
company will make equal annual
payments and expects that the fund will earn 12% year .How much
will be the amount of sinking fund
payment ?
NO
51 A television is purchased on installments basis such that tk.1,000 is to be
paid on the signing of the
contract and the balance in 6
yearly installment of tk.600 each payable at the end of each year . If
interest is charged at 8% .What
would be the cash down price.
NO
52 You have applied for a loan of tk.90,000 to purchase a new machine .You need
to make annual
payments of tk.17,254.25 at the
end of the next 10 years .What is the interest rate on this loan?
{PVA= A(FVIFA I, n,)}
NO
53 Determine the future values utilizing a time a preference rate 9%
a)
The future value of tk.15,000 invested now for a period of four years .
b)
The future value at the end of five years of an investments of
tk,6,000 now and an investment of
tk.6,000 one year from now.
c)
The future value at the end of eight years of an annual deposit of
tk.18,000 at the beginning of each year.
d)
The future value at the end of eight years of an annual deposit of
tk.18,000 at the beginning of each year.
NO
54 A machine cost a company tk.80,000 and its effective life is estimated to 15
years . If the scrap is
expected to realize tk.8,000 only
find the sum to be invested every year at 7% C. I. for 15 years to
replace the machine which is
expected to cost then 20% more over its present cost. ANS : 3,502
NO
55 A company sets aside for reserve fund the sum of tk.20,000 annually to
enable it to pay off a
debenture issue of tk.2,39,000 at
the end of 10 years . Assuming that the reserve accumulates at 4%
compounded find the surplus after
paying off the debenture stock. ANS 2,40122 & SURPLUS 1,122
NO
56 A man purchases a house and takes a mortgage on it tk.60,000 to be paid off
12 years by equal annual
payments . If the interest rate is
5% compounded annually what amount will be required to pay each
year? ANS A=6,769.52
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Md. Mursalin Sardar
Cell: 01925-425876
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