Question

At a simple interest rate of 12% per year, determine how long it will take $5000 to increase to twice as much.

Compare the time it will take to double if the rate is 20%.

Answer 1

To determine how long it will take $5000 to double at a 12% interest rate, we can solve the equation using compound interest formulas. It will take approximately 6 years and 3 months. If the interest rate is 20%, it will take approximately 3 years and 10 months.

Step-by-step explanation:

To determine how long it will take $5000 to increase to twice as much at a simple interest rate of 12% per year, we can use the formula for compound interest:

Principal (1 + interest rate) time = P(1 + r)^t

Let's assume it takes t years for $5000 to double:

$5000(1 + 0.12)^t = $10,000

Simplifying the equation:

1.12^t = 2

t = log(base 1.12) of 2

Using a calculator, we find that t is approximately 6 years and 3 months.

Now, let's compare the time it will take to double if the rate is 20%:

$5000(1 + 0.20)^t = $10,000

Simplifying the equation:

1.20^t = 2

t = log(base 1.20) of 2

Using a calculator, we find that t is approximately 3 years and 10 months.