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InterestSuppose A & B two business man. They are
doingbusiness. When A borrows money from B, then A hasto pay
certain amount of money to B for the use of themoney. The amount
paid by A is called Interest.Here borrowed amount is principal
Interest can be divided in two category:1. Simple interest2.
compound interest
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Simple interest When interest is payable on the principal only,
it iscalled simple interest.If I denotes the interest on a
principal P at an interestrate of r per year for n years, then we
have
I = Pnr
The accumulated amount A , the sum of the principal
and interest aftern
years is given by A = P + I = P + Prn
= P (1 +rn )
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Compound InterestFrequently, interest earned is periodically
added to theprincipal and thereafter earns interest itself at
thesame rate. This is called compound interest.Formula:I=
P(1+r)n
Where I= compound interest, P=principal amountr=rate of
interest, n=number of year.
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Annuity Certain(Payments are to be made for
a certain or fixed number of years)
Annuity Contingent (Payments are to be made till thehappening of
some contingentevent such as the death of aperson, marriage of a
girl ete.)
Annuity due(Where the first paymentfalls due at the beginningof
the ist interval, and soon)
Annuity immediate(Where the firstpayment falls due at theend of
the first interval,and so on)
Annuity Different types of annuities
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Calculation of different types of annuities:
1. Formula for the present value of an Annuity due
yearsofNumberinterestofRate
AnnuitydueAnnuityanofvaluePresent
where
n
i
A
V
i
iii
AV n ,1
111
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2. Formula for the present value of an Immediate Annuity
nii A
V 1
11
3. Formula for the amount of an Immediate Annuity
11 nii
A M
4. Formula for the amount of Annuity due
111n
iii
A M
5. Present Value of an Annuity
The present value of an Annuity is the sum of the present
values of its installments.
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Business applicability
A man borrows Tk. 6000 at 6% and promises to pay off theloan in
20 annual payments beginning at the end of the first year. What is
the annual payment necessary?
nii A
V 1
11
know,We
, where
V = Present value A = Annuity (annual payment)
i = Rate of interest
n = Number of years
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?
20
06.0100
6
000,6,
A
n
i
V Here
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19.523
19.523206.2
206.306.06000
206.3206.2
06.0
206.3
1206..3
06.0
206.3
11
06.0
06.1
11
06.0
06.01
11
06.0
6000
20
20
Tk.isnecessarypaymentannualThe
A
A
A
A
A
ALog (1.06)20
= 20 log 1.06=20 0.0253
=0.506 Antilog 0.506
=3.206(1.06)20
=3.206
