Question

Francine inherited $5,000 and plans to deposit the money in an account that compounds the interest monthly. If she can get 6% interest, the formula to calculate the amount of money in her account after t years is given by: t A 12  5000(1.005) How long will it take for her money to grow to $7,500?

Answer 1

To find how long it will take for Francine's money to grow to $7,500, we can set up the equation:

7500 = 5000(1.005)^(12t)

where t is the number of years. We want to solve for t.

First, divide both sides by 5000:

1.5 = (1.005)^(12t)

Next, take the natural logarithm of both sides:

ln(1.5) = ln(1.005)^(12t)

Using the rule of logarithms that ln(a^b) = b ln(a), we can simplify the right side:

ln(1.5) = 12t ln(1.005)

Finally, divide both sides by 12 ln(1.005):

t = ln(1.5)/(12 ln(1.005))

Using a calculator, we get:

t ≈ 14.6 years

Therefore, it will take about 14.6 years for Francine's money to grow to $7,500.