calculating interest earned over time\nwhen rahul began 7th grade, he put his savings of $3,000 in an…

calculating interest earned over time\nwhen rahul began 7th grade, he put his savings of $3,000 in an account that compounded interest annually. he hoped to have $6,000 by the time he graduates high school in six years. what interest rate is required for him to reach his goal?\nan interest rate of % is required.

calculating interest earned over time\nwhen rahul began 7th grade, he put his savings of $3,000 in an account that compounded interest annually. he hoped to have $6,000 by the time he graduates high school in six years. what interest rate is required for him to reach his goal?\nan interest rate of % is required.

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. We know that $P=$3000$, $A = $6000$, and $t = 6$. Substitute these values into the formula: $6000=3000(1 + r)^6$.

Step2: Simplify the equation

Divide both sides of the equation by 3000: $\frac{6000}{3000}=(1 + r)^6$, which simplifies to $2=(1 + r)^6$.

Step3: Solve for $r$

Take the sixth - root of both sides: $1 + r=2^{\frac{1}{6}}$. $2^{\frac{1}{6}}\approx1.1225$. Then $r=2^{\frac{1}{6}}-1\approx1.1225 - 1=0.1225$.

Step4: Convert $r$ to a percentage

Multiply $r$ by 100 to get the percentage: $r\times100 = 12.25%$.

Answer:

$12.25$