Suppose that $2000 is placed in a savings account at an annual rate of 5.6%, compounded semiannually. Assuming that no withdrawals are made, howlong will it take for the account to grow to $22967Do not

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TofuMaster asked Oct 8, 2023

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21 votes

Suppose that $2000 is placed in a savings account at an annual rate of 5.6%, compounded-example-1

Mathematics
college

TofuMaster asked Oct 8, 2023

by TofuMaster

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1 Answer

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$\begin{gathered} t=(\ln((A)/(P)))/(n\lbrack\ln(1+(r)/(n))\rbrack) \\ \text{Given} \\ A=2296 \\ P=2000 \\ r=0.056 \\ n=2 \\ \text{Substitute} \\ t=(\ln((A)/(P)))/(n\lbrack\ln(1+(r)/(n))]) \\ t=(\ln((2296)/(2000)))/(2\lbrack\ln(1+(0.056)/(2))\rbrack) \\ \text{ Input in a scientific calculator and we get} \\ t=2.5\text{ years} \end{gathered}$