Question

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%. How long will it take for her

Answer 1

Answer:

It will take 36.1 years for her money to reach $105,000.

Step-by-step explanation:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.

This means that $P(0) = 7000, r = 0.075$

How long will it take for her money to reach $105,000?

This is t for which P(t) = 105000.

$P(t) = P(0)e^{rt}$

$105000 = 7000e^{0.075t}$

$e^{0.075t} = \frac{105000}{7000}$

$e^{0.075t} = 15$

$\ln{e^{0.075t}} = \ln{15}$

$0.075t = \ln{15}$

$t = \frac{\ln{15}}{0.075}$

$t = 36.1$

It will take 36.1 years for her money to reach $105,000.