After how many years will an investment of $100 compounded quarterly at 6% annually be worth $450? (round to the nearest year)

Question

After how many years will an investment of $100 compounded quarterly at 6% annually be worth $450? (round to the nearest year)

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Minh Khuê 4 years 2021-07-28T10:55:36+00:00 1 Answers 10 views 0

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  1. diemkieu
    0
    2021-07-28T10:56:54+00:00
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    Answer:

    The investment will be worth $450 after 25.255 years which is about 25 years and 3 months.

    Step-by-step explanation:

    You have to use the following formula to calculate the number of years:

    t=ln(A/P) / n(ln(1 + r/n)), where:

    t=time in years

    A=Accrued amount=450

    P=Principal amount=100

    n=number of compounding periods per time period=4

    r=interest rate=0.06

    Now, you can replace the values in the formula:

    t=ln(450/100)/4(ln(1+(0.06/4)))

    t=ln(4.5)/4(ln(1.015))

    t=1.50/0.059

    t=25.255

    According to this, the answer is that the investment will be worth $450 after 25.255 years which is about 25 years and 3 months.

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