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4 years ago

Using the chart above, find the total amount and amount of interest paid in the following compound interest problems.

Mathematics

1 answer:

gizmo_the_mogwai [7]4 years ago

6 0

Answer:

Annually: Total Amount = 1611.76, Interest Amount = 711.76

Semiannually: Total Amount = 1625.50 , Interest Amount = 725.50

Quarterly: Total Amount = 1632.62 , Interest Amount = 732.62

Step by Step Explanation:

We can see from the table that the factor that we need to multiply with 900 in order to get amount for compounded annually is 1.7908477. Therefore, our total amount is 1.7908477*900 = 1611.76 and interest earned is 1611.76-900 = 711.76.

The factor that we need to multiply with 900 in order to get amount for compounded semiannually is 1.8061112. Therefore, our total amount is 1.8061112*900 = 1625.50 and interest earned is 1625.50-900 = 725.50.

The factor that we need to multiply with 900 in order to get amount for compounded semiannually is 1.8140184. Therefore, our total amount is 1.8140184*900 = 1632.62 and interest earned is 1632.62-900 = 732.62.

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3 years ago

find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

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$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - A trapezium ABCD with non parallel sides of measure 15 cm each ! along , the parallel sides are of measure 13 cm and 25 cm

To find - Area of trapezium

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

Construction -

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

Since we've obtained the height now , we can easily find out the area of trapezium !

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

hope helpful :D

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2 years ago