Find the time required for an investment to double in value if invested in an account paying 3% compounded quarterly.

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Find the time required for an investment to double in value if invested in an account paying 3% compounded quarterly.

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Thu Thủy 4 years 2021-07-19T06:56:37+00:00 1 Answers 7 views 0

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  1. thuthao
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    2021-07-19T06:57:52+00:00
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    Answer: 6.12\ \text{years}

    Step-by-step explanation:

    Given

    Rate of interest is r=3\% compounded quarterly

    So, annually it is r=12\%

    Suppose P is the Principal and A is the amount after certain time period.

    Amount in Compound interest is given by

    \Rightarrow A=P[1+r\%]^t

    for given conditions

    \Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=\dfrac{\ln (2)}{\ln (1.12)}\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}

    It take 6.12\ \text{years} to double the invested amount.

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