Question

Javier wants to invest $6400 in a savings account. Determine the interest rate (simple interest)required for Javier's investment to double in value in 14 years. Round your answer to the nearesttenth of a percent.Answer:%

Answer 1

It is given that $6400 was invested for 14 years at a simple interest rate.

It is required to find the interest rate needed for the investment to double in 14 years.

The amount for simple interest is given by the formula:

$A=P(1+rt)$

Where A is the final amount after the period of investment.

P is the amount invested.

r is the interest rate.

t is the number of years.

Since the investment needs to be doubled, it follows that:

$A=2P$

Substitute A=2P into the simple interest formula:

$2P=P(1+rt)$

Substitute t=14 into the equation and solve for r:

$\begin{gathered} 2P=P(1+14r) \\ \text{ Divide both sides by }P: \\ \Rightarrow\frac{2P}{P}=\frac{P}{P}(1+14r) \\ \Rightarrow2=1+14r \\ \text{ Subtract }1\text{ from both sides:} \\ \Rightarrow2-1=1+14r-1 \\ \Rightarrow1=14r \\ \text{ Swap the sides:} \\ \Rightarrow14r=1 \\ \text{ Divide both sides by }14: \\ \Rightarrow\frac{14r}{14}=\frac{1}{14} \\ \Rightarrow r=\frac{1}{14} \end{gathered}$

Convert the rate to a percentage by multiplying by 100%:

$r=\frac{1}{14}\times100\%\approx7.1\%$Answer: 7.1%.