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olga55 [171]
3 years ago
6

if you deposit 4500 at 5% annual interest compounded annually how much money will be in the account after 30 months

Mathematics
1 answer:
Alja [10]3 years ago
8 0

Answer:

A = $ 50,978.44

Step-by-step explanation:

First, convert R percent to r a decimal

r = R/100

r = 5%/100

r = 0.05 per year,

Then, solve our equation for A

A = P(1 + r/n)nt

A = 45,000.00(1 + 0.004166667/12)(12)(2.5)

A = $ 50,978.44

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<h2>\bf \purple{ \underline{Given :-}}</h2>

• \:  {( \sqrt{3} )}^{x + y}  = 9\:  \:  \: \: (i)

• \:  {( \sqrt{2} )}^{x - y}  = 32 \:  \:  \: \: (ii)

\\

<h2>\bf \purple{ \underline{To  \: Find :- }}</h2>

•   {\sf{The  \: value  \: of}} \:   \: 2x+ y.

\\

\huge\bf \purple{ \underline{Solution :- }}

\sf{From \:  equation \:  (i), }

{( \sqrt{3} )}^{x + y}  = 9

⇒ {( \sqrt{3} )}^{x + y}  =  ({ \sqrt{3} })^{4}

⇒ x + y = 4 \:  \:  \: \: (iii)

\\

\sf{From \:  the  \: equation \:  (ii)}

{( \sqrt{2} )}^{x - y}  = 32

⇒( { \sqrt{2} })^{x - y}  =(  { \sqrt{2} })^{10}

⇒x - y = 10 \:  \:  \: \: (iv)

\\

\sf{We \:  have \:  to  \: add \:  equation \:  (iii)  \: and \:  equation  \: (iv)}

x + y + x - y = 4 + 10

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⇒x = 7

\\

\sf{Subtracting \:  equation \:  (iii)  \: from  \: equation  \: (ii),  }

x  - y - x - y = 10 - 4

⇒ - 2y = 6

⇒y =  - 3

\\

\bf\therefore x = 7 \: \:  and  \: \: y =  - 3

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{ \sf{Th e \:  value \:  of }}= 2x +y

\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:   \: =2 \times 7  + ( - 3)

\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:   \: =14 - 3

\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:   =11

\bf \red{Hence,  \: the  \: value \:  of  \: 2x + y  \: is  \: 11. }

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