Question

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include a comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your two decimal places, show both decimal places (5.06). how long does it take $450 to double at a simple interest rate of 14%? express your answer in months. round to the nearest whole number.

Explanation:

Step1: Determine the final amount

The initial amount $P = 450$, and we want it to double, so the final amount $A=2\times450 = 900$. The simple - interest formula is $A=P(1 + rt)$, where $r$ is the annual interest rate and $t$ is the time in years. First, we find the interest amount $I=A - P$. So $I=900 - 450=450$.

Step2: Use the simple - interest formula $I = Prt$

We know that $P = 450$, $r=0.14$ (since $14\%=0.14$), and $I = 450$. Substitute these values into the formula $I = Prt$. We get $450=450\times0.14\times t$.

Step3: Solve for $t$ (in years)

Divide both sides of the equation $450=450\times0.14\times t$ by $450\times0.14$. So $t=\frac{450}{450\times0.14}=\frac{1}{0.14}\approx7.1429$ years.

Step4: Convert years to months

Since there are 12 months in a year, the number of months $n = 12t$. So $n=12\times7.1429\approx86$ months.

Answer:

86