##### Finance question for math

label Mathematics
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How long will it take for \$99,000 to grow to \$45,700 at an interest rate of 12.4% if the interest compounded continuously? Round the number of years to the nearest hundredth.

Jul 21st, 2015

I am assuming that there was a mistake in the question and that question is like this

How long will it take for \$45,700 to grow to \$99,000 at an interest rate of 12.4% if the interest compounded continuously?

If my interpretation is wrong please do tell me and I shall correct my answer

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Principal, P = \$45,700

Amount, A = \$99,000

Rate of interest, r = 12.4% = 12.4/100 = 0.124

Time, t = ?

The compound interest formula for continuous compounding is

$\\ A=Pe^{rt}\\ \\$

Substitute the values of A, P and r into the equation

$\\ 99000=45700e^{0.124t}\\ \\ \frac{99000}{45700}=e^{0.124t}\\ \\ \frac{990}{457}=e^{0.124t}\\ \\ Take\hspace{5}natural\hspace{5}logarithm\hspace{5}on\hspace{5}both\hspace{5}sides\\ \\ ln\bigg(\frac{990}{457}\bigg)=ln(e^{0.124t})\\ \\ ln\bigg(\frac{990}{457}\bigg)=0.124t\times ln(e)\\ \\ ln\bigg(\frac{990}{457}\bigg)=0.124t\times1\\ \\ ln\bigg(\frac{990}{457}\bigg)=0.124t\\ \\ 0.124t=ln\bigg(\frac{990}{457}\bigg)\\ \\ t=\frac{ln\bigg(\frac{990}{457}\bigg)}{0.124}\\ \\ t=6.23\hspace{5}years$

ANSWER: Time, t = 6.23 years

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Jul 21st, 2015

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Jul 21st, 2015
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Jul 21st, 2015
Jun 24th, 2017
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