interest compound interst and annuities.

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4. Interest
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5. 

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The amount paid at stated rate for use of money for specific time.
we can also say that the rent.Simple interest is most often used for
loans of shorter duration.
Charge of borrowed money at annual percentage rate is interest.
The money borrowed in a loan is called the principal.
The number of dollars received by the borrower is the present
value.
In a simple interest loan, the principal and present value are the
same.
The interest rate is the fee for a simple interest loan and usually is
expressed as a present of the principal.
Simple interest is paid on the principal borrowed and not paid on
interest already earned.
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6. The simple interest of a loan can be calculated
using the following formula.
P = principal (amount borrowed)
r = interest rate per year (in decimal form)
t = time in years.
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7.  Find
simple interest on an amount of Rs 800
in 8 month’
As we know formula
I= 800*.05*8/12= 26.67 answer
Hence interest is 26.67
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8. An individual borrows $300 for 6 months at 1% simple interest per
month. How much interest is paid?
Remember to check that r and t are consistent in time units. Here, it
will be months.
I = Prt = 300 0.01 6 = $18
Assume you invest $1,000 at 6% simple interest for 3
years.
($1,000 .06 3 = $180)
(or $60 each year. You would earn $180 interest.
for 3 years)
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9. where I is the amount of interest, P is the
principal (amount of money borrowed), r
is the interest rate (per year), and t is the
time (expressed in years). The formula
can also be expressed as:
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10. 
A loan made at simple interest requires that the borrower
pay back the sum borrowed (principal) plus the interest.
This total is called the future value, or amount and is equal
to P + I.
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where
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P + Prt
P(1 + rt)
P = principal or present value
r = annual interest rate (in decimal form)
t = time in years
A = amount or future value
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11. Find the future value of $460 in 8
months, if the annual interest rate
is 12%.
A = P (1 + rt )
If you can earn 6% interest, what lump sum
must be deposited now so that its value will
be $3500 after 9 months?
A = P (1 + rt )
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13. 
Interest paid on principal plus interest is called
compound interest
it can be done semiannually, quarterly, monthly, or
daily. This time interval is called the compounding
period (or the period).
Compound interest is based on the principal
which changes from time to time
 The unpaid interest is added to the principal
balance and becomes part of the new principal
balance for the next interest period.
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14. Period
Interest
Credited
Times
Credited
per year
1
Rate per
compounding
period
R
Annual
year
Semiannual
6 months 2
R
2
Quarterly
quarter
4
R
4
Monthly
month
12
R
12
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15. Amount : Compound Interest
 Where and
 A = amount or future value at the end of n periods
 P = principal or present value
 r = annual nominal rate
 m = number of compounding periods per year
 i = rate per compounding period
 n = total number of compounding periods
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17. 
Suppose $800 is invested at 6%, and it is compounded
annually. What is the amount in the account at the end
of 4 years?
`
First, determine the information that is given
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There will be $1009.98 in the account after 4 years.
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18. 
The general formula for finding the amount after a specified
number of compound periods is
where r = annual interest rate
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m = number of times compounded per year
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i = r/m = interest rate per period
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n = mt, the number of periods, where t is the number of years
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A = amount (future value) at the end of n compound periods
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P = principal (present value)
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19. 
Interest earned on the
principal investment
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Earning interest on interest
Principal plus interest
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20. the difference between
simple interest and
compound interest on a
certain sum is Rs 250for
two years at 5% P.a find
the sum?
T= 2 years
R=.05
P=?
I=PRT
P=.05*2
I=.10
C.I=P(1+I^N)-1
C.I=10(1+.05^2)-1
C.I=.1025
C.I –S.I
0.1025-.10=.0025
250/.0025=10000
The sum is 10000
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22. a sequence of payments made at regular time
intervals.
payments made at the end of each payment period.
payment period coincides with the interest conversion period.
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23.  The
future value S of an annuity of n
payments of R dollars each, paid at the
end of each investment period into an
account that earns interest at the rate of
i per period is
S
R
(1
i)
n
1
i
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24. 
The present value P of an annuity of n
payments of R dollars each, paid at the end
of each investment period into an account
that earns interest at the rate of i per period
is
P
R
1
(1
i)
n
i
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