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Simple interest is given by the formula A = P + P r t A = P + P r t . Where A A is the balance of the account after t t years, and P P is the starting principal invested at an annual percentage rate of r r , expressed as a decimal. Dustin is investing money into a savings account that pays 5% simple interest, and plans to leave it there for 10 years. Determine what Dustin needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years. Dustin will have to invest $ now in order to have a balance of $20,000 in his savings account after 10 years. Round your answer to the nearest dollar.

Answer :

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ \begin{array}{llll} A=P+Prt\\\\ A=P(1+rt) \end{array} \qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$20000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &10 \end{cases} \\\\\\ 20000=P(1+0.05\cdot 10)\implies 20000=P(1.5) \\\\\\ \cfrac{20000}{1.5}=P\implies 13333.\overline{3}=P\implies \stackrel{\textit{rounded up}}{13333=P}[/tex]

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