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Rashid [163]
3 years ago
14

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

Mathematics
1 answer:
NeX [460]3 years ago
6 0

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.

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