##### how long will it take for an investment to grow?

label Calculus
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schedule 1 Day
account_balance_wallet \$5

Oct 21st, 2017

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Principal, P = \$7,000

Amount, A = \$10,000

Rate of interest, r = 3% = 0.03

Number of times interest is compounded per year = 365

Time, t = ?

The compound interest formula is

$\\ A=P\bigg(1+\frac{r}{n}\bigg)^{nt}\\ \\ 10000=7000\bigg(1+\frac{0.03}{365}\bigg)^{365t}\\ \\ \frac{10000}{7000}=\bigg(1+\frac{0.03}{365}\bigg)^{365t}\\ \\ \frac{10}{7}=\bigg(1+\frac{0.03}{365}\bigg)^{365t}\\ \\ Take\hspace{5}logarithm\hspace{5}on\hspace{5}both\hspace{5}sides\\ \\ log\bigg(\frac{10}{7}\bigg)=log\bigg(1+\frac{0.03}{365}\bigg)^{365t}\\ \\ log\bigg(\frac{10}{7}\bigg)=365t\times log\bigg(1+\frac{0.03}{365}\bigg)\\ \\ 365t\times log\bigg(1+\frac{0.03}{365}\bigg)=log\bigg(\frac{10}{7}\bigg)\\ \\ t=\frac{log\bigg(\frac{10}{7}\bigg)}{365log\bigg(1+\frac{0.03}{365}\bigg)}\\ \\ t=11.89\hspace{5}years$

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Jul 9th, 2015

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Oct 21st, 2017
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Oct 21st, 2017
Oct 22nd, 2017
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