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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