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3 votes
At the beginning of year 1, Sam invests $700 at an annual compound interest

rate of 5%. He makes no deposits to or withdrawals from the account.
Which explicit formula can be used to find the account's
beginning of year 4? What is the balance?

At the beginning of year 1, Sam invests $700 at an annual compound interest rate of-example-1
User Didgeridoo
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1 Answer

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at the beginning of year 4, only 3 years have elapsed, the 4th year hasn't started yet, since it's at the beginning, so at the beginning of year 4 we can say only 4-1 years have elapsed.


~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$700\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=\textit{elapsed years}\dotfill &3 \end{cases}


A=700\left( 1 + (0.05)/(1) \right)^(1\cdot 3)\implies A = 700(1+0.05)^3\implies A(4)=700(1+0.05)^(4-1) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A(n)=700(1+0.05)^(n-1)~\hfill

User Nicolaspanel
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