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aivan3 [116]
3 years ago
12

Your grandparents invested $2,000 for you on the day you were born. How much will this investment be worth on your 25th birthday

if the money was invested in a savings account averaging an annual yield of 5% and the interest is compounded quarterly?
Please answer this correctly.​
Mathematics
1 answer:
algol [13]3 years ago
8 0

We know that, Amount in Compound interest is given by :

\bigstar \ \ \boxed{\sf{Amount = Principal\bigg(1 + \dfrac{Rate \ of \ Interest}{100}\bigg)^{Time \ Period}}}

Given : Principal = $2000

Given : Annual yield is 5% and the interest is compounded quarterly

It means : Interest is compounded 4 times in a year

\implies \sf{Rate \ of \ Interest = \dfrac{R}{4} = \dfrac{5}{4}}

\sf{\implies Time \ period = (25 \times 4) = 100}

Substituting all the values in the formula, we get :

\implies \sf{Amount = 2000\bigg(1 + \dfrac{\dfrac{5}{4}}{100}\bigg)^{100}}

\implies \sf{Amount = 2000\bigg(1 + \dfrac{5}{400}\bigg)^{100}}

\implies \sf{Amount = 2000\bigg(1 + \dfrac{1}{80}\bigg)^{100}}

\implies \sf{Amount = 2000\bigg(\dfrac{81}{80}\bigg)^{100}}

\implies \sf{Amount = 2000 \times (1.0125)^{100}}

\implies \sf{Amount = 2000 \times 3.463}}

\implies \sf{Amount = 6926.8}

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jeka57 [31]
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Distance from origin = 8

Let equation be Ax+By+C=0
then -A/B=-&radic;3, or
B=A/&radic;3.
Equation becomes
Ax+(A/&radic;3)y+C=0

Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/&radic;3)y+C)/sqrt(A^2+(A/&radic;3)^2))
Substitute coordinates of origin (x,y)=(0,0)  =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
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Therefore one solution is
x+(1/&radic;3)+(16/3)&radic;3=0
or equivalently
&radic;3 x + y + 16 = 0

Check:
slope = -1/&radic;3  .....ok
distance from origin
= (&radic;3 * 0 + 0 + 16)/(sqrt(&radic;3)^2+1^2)
=16/2
=8  ok.

Similarly C=-16 will satisfy the given conditions.

Answer  The required equations are
&radic;3 x + y = &pm; 16 
in standard form.

You can conveniently convert to point-slope form if you wish.




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