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If you had invested ​$3000 on January​ 1st, 2009, at 6​% interest compounded ​, how much would you have on April ​1, 2018​?

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answer:

To calculate the future value of an investment with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal amount (initial investment)

r = annual interest rate (in decimal form)

n = number of times the interest is compounded per year

t = number of years

Given:

P = $3000

r = 6% = 0.06 (decimal form)

n = 1 (compounded annually)

t = 2018 - 2009 = 9 years

Step 1: Plug in the values into the formula:

A = 3000(1 + 0.06/1)^(1*9)

Step 2: Simplify the calculation:

A = 3000(1 + 0.06)^9

Step 3: Calculate the value inside the parentheses first:

A = 3000(1.06)^9

Step 4: Evaluate the exponential term:

A ≈ 3000 * 1.619

A ≈ $4857

Therefore, if you had invested $3000 on January 1st, 2009, at a 6% interest compounded annually, you would have approximately $4857 on April 1, 2018.

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