Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
Let's start with the first investment of $4000:
A1 = 4000(1 + 0.06/1)^(1*9)
= 4000(1.06)^9
= $6,542.51
Now, let's move on to the second investment of $7000, made four years from now:
A2 = 7000(1 + 0.06/1)^(1*5)
= 7000(1.06)^5
= $9,381.81
Finally, let's calculate the third investment of $5000, made six years from now:
A3 = 5000(1 + 0.06/1)^(1*3)
= 5000(1.06)^3
= $5,674.32
The total amount after 9 years will be the sum of these three amounts:
Total = A1 + A2 + A3
= $6,542.51 + $9,381.81 + $5,674.32
= $21,598.64
Therefore, the total amount after 9 years will be $21,598.64.