When Raul began seventh grade he put his savings of $3000 in an account that compounds interest annually. He hopes to have $6000 by the time he graduates high school in six years. What interest rate is required for him to reach his goal?

  12.25%

Step-by-step explanation:

Raul needs to find the value of r such that ...

  A = P(1 +r)^t . . . . . formula for future value of P at interest rate r

  6000 = 3000(1 +r)^6 . . . . with given numbers

  2 = (1 +r)^6 . . . . . . . . . . . . . divide by 3000

  2^(1/6) = 1 +r . . . . . . . . . . . . take the 6th root

  2^(1/6) -1 = r ≈ 0.1225 = 12.25%

Raul needs an interest rate of 12.25% to reach his goal.

Check

Raul wants to double his money in 6 years. The "rule of 72" says the product of doubling time and percent interest rate is about 72. For a 6-year doubling time, that suggests Raul needs an interest rate of about 72/6 = 12 percent. This is close to what we calculated.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

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