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How long will it take for a $5000 investment to grow to $5925 at an annual rate of 3%, compounded monthly? Assume that no withdrawals are made.Do not round any intermediate computations, and round your
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How long will it take for a $5000 investment to grow to $5925 at an annual rate of 3%, compounded monthly? Assume that no withdrawals are made.Do not round any intermediate computations, and round your answer to the nearest hundredth

How long will it take for a $5000 investment to grow to $5925 at an annual rate of-example-1
User FredRoger
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\begin{gathered} \text{ The formula for compound interest is} \\ A=P(1+(r)/(n))^(nt) \\ \text{ Rearranging the formula so that we solve for time and we get} \\ t=(\ln ((A)/(P)))/(n\lbrack\ln (1+(r)/(n))\rbrack) \\ \text{The given that we have are} \\ P=5000 \\ A=5925 \\ r=0.03\text{ this is derived from 3\% converted to decimal} \\ n=12\text{ Since this is compounded monthly} \\ \text{Substitute the following values and we have} \\ t=(\ln((A)/(P)))/(n\lbrack\ln(1+(r)/(n))]) \\ t=(\ln ((5925)/(5000)))/(12\lbrack\ln (1+(0.03)/(12))\rbrack)\text{ Input this in a scientific calculator and we get} \\ t=5.67\text{ years, rounded off to the nearest hundredth} \end{gathered}

How long will it take for a $5000 investment to grow to $5925 at an annual rate of-example-1
User Squirrelsareduck
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