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Alina [70]
4 years ago
6

gavin deposited $1500 into his savings account that is compounded quarterly at an interest rate of 1.5%. How munch money will ga

vin have after 5 years?
Mathematics
1 answer:
creativ13 [48]4 years ago
4 0

<u>Answer:</u>

The money will gavin have after 5 years is 1616.59$

<u>Explanation:</u>

We know that compound interest is given by  

A=P\left(1+\frac{r}{n}\right)^{n t}

          Where A = final amount

       P = Principal amount = $1500 (given)

r  = interest rate = 1.5% = 0.015

n = no. of times interest applied per time period = given quarterly = 4

t = time period = 5 years  

    So,

A=1500\left(1+\frac{0.015}{4}\right)^{4 \times 5}

1500\left(1+\frac{0.015}{4}\right)^{20}

 = 1616.59$ which is the money will gavin have after 5 years

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Let's say that x is the total amount invested by all three.

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\bold{\huge{\underline{ Solution }}}

<h3><u>Given </u><u>:</u><u>-</u></h3>

  • We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

<h3><u>To</u><u> </u><u>Find </u><u>:</u><u>-</u></h3>

  • <u>We </u><u>have </u><u>to </u><u>calculate </u><u>the </u><u>length </u><u>of </u><u>the </u><u>sides </u><u>of </u><u>given </u><u>triangle </u><u>and </u><u>also </u><u>we </u><u>have </u><u>to </u><u>determine </u><u>whether </u><u>it </u><u>is </u><u>right </u><u>angled </u><u>triangle </u><u>or </u><u>not </u>

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>Here</u><u>, </u><u> </u><u>we </u><u>have </u>

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  • Coordinates of Q = ( x2 = 6 , y2 = 1 )
  • Coordinates of R = ( x3 = 2 , y3 = 9 )

<u>By </u><u>using </u><u>distance </u><u>formula </u>

\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}

<u>Subsitute </u><u>the </u><u>required </u><u>values </u><u>in </u><u>the </u><u>above </u><u>formula </u><u>:</u><u>-</u>

Length of side PQ

\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}

\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}

\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}

\sf{ = }{\sf\sqrt{ 100 + 25 }}

\sf{ = }{\sf\sqrt{ 125 }}

\sf{ = 5 }{\sf\sqrt{ 5 }}

Length of QR

\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}

\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}

\sf{ = }{\sf\sqrt{16 + 64 }}

\sf{ = }{\sf\sqrt{80 }}

\sf{ = 4 }{\sf\sqrt{5 }}

Length of RP

\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}

\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}

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\sf{ = }{\sf\sqrt{ 45 }}

\sf{ = 3}{\sf\sqrt{ 5 }}

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\bold{ PQ^{2} + QR^{2} = PR^{2}}

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>,</u>

\bold{  125 + 80 = 45 }

\bold{  205  = 45 }

<u>From </u><u>above </u><u>we </u><u>can </u><u>conclude </u><u>that</u><u>, </u>

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