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Andrei [34K]
3 years ago
15

Suppose you invest $150 a month for 5 years into an account earning 7% compounded monthly. After 5 years, you leave the money, w

ithout making additional deposits, in the account for another 23 years. How much will you have in the end?
Mathematics
1 answer:
lisabon 2012 [21]3 years ago
7 0

Answer:

About 0.3 billion dollars

Step-by-step explanation:

5 years = 60 months.

The 150 of the first month will be 150*1.07^60 in 5 years.

The 150 of the second month will be 150*1.07^59 in 5 years.

The 150 of the third month will be 150*1.07^58 in 5 years.

And so forth.

So we sum that up:

( sum_(n=1)^(60) 150×1.07^n)

And multiply with

× 1.07^(5×23)

to account for the increase in value in the following 23 years.

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Move 1 to the left side of the equation by subtracting it from both sides.

\sqrt{2x -5 - 2 - 1 = 0 }

Subtract 1 from -2.

\sqrt{2x -5 - 3 = 0 }

Add 3 to both sides of the equation.

\sqrt{2x - 5 = 3}

To remove the radical on the left side of the equation, square both sides of the equation.

\sqrt{2x - 5^3 = 3^2}

Simplify each side of the equation.

Multiply the exponents in (( 2x - 5) ^\frac{1}{2})^2 .

Apply the power rule and multiply exponents, (a^m)^n = a^mn

(2x -5)^\frac{1}{2}.2 = 3^2

Cancel the common factor of 2.

(2x - 5)^1 = 3^2

Simplify.

2x - 5 = 3^2

Raise 3 to the power of 2.

2x - 5 = 9

Solve for x

Move all terms not containing x to the right side of the equation.

Add 5  to both sides of the equation.

2x = 9 + 5

Add 9 and 5.

2x = 14

Divide each term by 2  and simplify.

Divide each term in 2x = 14 by 2.

\frac{2x}{2} = \frac{14}{2}

Cancel the common factor of 2.

x = \frac{14}{2}

Divide 14 by 2.

x = 7

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