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March 28, 2017

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If you deposit P dollars into a bank account paying an annual interest rate r, with n interest payments each year, the amount A you would have after t years is A=P(1+r/n)^nt. Kevin places $100 in a savings account earning 6% annual interest, compound quarterly. If Kevin adds no more money to his account, how long will it take his money to double?

  • Math - ,

    P = Po(1+r)^n.

    r = (6%/4)/100% = 0.015 = Quarterly %
    rate expressed as a decimal.

    n = 4comp/yr * t = 4t.

    P = 100(1.015)^4t = 200
    (1.015)^4t = 200/100 = 2.00
    4t*Log1.015 = Log2
    4t = Log2/Log1.015 = 46.556
    t = 11.64 Yrs.

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