Algebra

An investment account earns 7.5% per year compounded quarterly. How many years will it take for the account to triple its initial value. (Make sure that you round up)

For the death of me, I can't figure out how to do this problem. Can anybody walk me through it so I can do the others? Thanks!

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  1. four times a year so every 1/4 year multiply by 1 + .075/4 = 1.01875
    do that for n years or in other words 4n periods
    so
    3 = (1.01875)^4n
    log 3 = 4n log 1.01875
    I suspect you can take it from there.

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  2. Lovely! Thank you so much Damon! <3

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  3. You must be familiar and know by heart the compound interest formula:

    Amount = principal(1 + i)^n , where i is the periodic interest rate expressed
    as a decimal, and n is the number of interest periods.

    in your case i = .075/4 = .01875
    and n = ??
    amount = 3, principal = 1

    then : 1(1.01875)^n = 3
    you will need to use logs to solve this problem.
    Let me know what you get.

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  4. The Accumulated amount needs to triple...
    Do you know how to "undo" an exponent?
    AKA do you know how to use logarithms?
    If not... I will show you without them : )

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  5. MsPi, No, I do not know how to use logarithms. thanks :)

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  6. Reiny I don't even recall learning interest as I moved schools in the middle of the year when we started studying them.

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  7. So if you call your principal 1, then to triple it, it would need to grow to 3.
    Thus the accumulated amount in the account would need to grow to 3.
    Given
    A=P(1+i)^n
    3 = 1(1 + 0.075/4)^4n
    3=(1.01875)^4n
    since you can't recall logarithms (and may have missed that section of learning due to your school move).
    start with n=1
    3=(1.01875)^4(1)
    now sub the right hand side into your calculator and see if it equals three
    but the right hand side equals 1.077135 when n=1,
    so continue in this manner until the right hand side is equal to 3,
    let's try n=10
    (1.01875)^4(10)
    =2.1023
    So we are not yet at 3, and have to continue to increase the number of times the money is looked at.
    Let me know what you get : )
    (

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