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ALGEBRA
- solved problems
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Interest
calculations |
Simple interest
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111. |
Somebody deposits $20,000 into a savings account
where the rate of interest is 4.8% annually.
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How much money in interest will earn after nine months?
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An amount of money deposited into a bank for a given period of
time brings to the depositor a profit called interest.
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The
amount of
interest (I
) the bank pays you, depends on the
interest rate (
i % ),
the amount of money deposited, denoted as principal P
also called original balance (or
initial investment), and the period of
time n
the money is deposited, |
since P
: 1 = I : (i · n)
then, |
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Solution:
Given,
P
= $20000 ,
p%
= 4.8% and n
= 9
months,
I
=
?
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112. |
A bank lends a company money for the six months period at
a rate of 8% annually.
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How much was lent if the company should pay $12,000 of interest?
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Solution:
Given,
I
= $12000 ,
p%
= 8% and n
= 6 months,
P
=
?
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113. |
At what an interest rate was borrowed
$75,000 for one year if $3,000 to interest is charged?
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Solution:
Given,
P
= $75000 ,
I
= $3000
and n
= 1 year,
i
=
?
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114. |
For what period of time should be deposited
$200,000 at a 6% interest rate to earn $6,000
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of interest?
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Solution:
Given,
P
=
$200,000
, p%
= 6%
and I
= $6,000,
n
=
?
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Compound interest |
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115. |
If $10,000 is invested for
five years at 6% of the interest rate, find the accumulated or
final value and
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total interest earned at the end of the period
under both, simple and compound interest. |
In compound interest calculations,
the interest earned in each period is added at the end of a
period to the principal of the previous period, to become the
principal for the next period. |
The compounding periods can be yearly, semiannually, quarterly,
or the interest can be compounded more frequently even continuously. |
If
P
is the principal or initial value of investment, A
is the accumulated amount or final value of investment and the compound interest
rate is i % |
then,
A = P · r
n,
where r
= 1 + i,
and where |
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Solution:
Given,
P
= $10,000, p%
= 6%
and
n =
5 years, A and
I
=?
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a)
Under simple interest,
the total interest earned in five years period is |
I = i% · P · n =>
I = 6/100
· 10000 · 5 = $3000, |
the accumulated value after five years period is |
A
= P + I = P (1 + i n) =>
A
= 10000 · (1 + 6/100 · 5) = 10000
· 1.3 = $13000, |
so
that I
= A -
P
= 13000
-
10000 = $3000. |
b) Under compound interest,
the accumulated value after five years period is |
A
= P(1 + i%)n
=> A
= 10000 · (1 + 0.06)5
= 10000 · 1.338225 = $13382.25 |
therefore, the total interest earned in five years period is |
I
= A -
P
= 13382.25
-
10000 =
$3382.25. |
So,
the interest compounding (or interest earned on interest) brings
the extra $382.25 in
comparison with the simple interest. |
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116. |
After how many years will
deposit double at an interest rate of 6%.
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Solution: |
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117. |
At what annual interest
has to be deposited $5,000 for four years to grow to $8,000.
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Solution: |
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