Math Compound Interest

If $500 is invested at an interest rate of 4.5% per year, find the amount of the investment at the end of 11 years for the following compounding methods. (Round your answers to the nearest cent.)

Find a, Anually
Find b, SemiAnually
Find c, Quarterly
Find d, Continuosly

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  1. a. P = Po(1+r)^n.
    Po = $500.
    r = 0.045/yr. = Annual % rate.
    n = 1Comp/yr. * 11yrs. = 11Compounding periods.

    b. r = 0.045/yr. * 0.5yr. = 0.0225 = Semi-annual % rate.
    n = 2Comp./yr. * 11yrs. = 22 Compounding periods.

    c. r = 0.045/yr. * 0.25yr. = 0.01125 = Quarterly % rate.
    n = 4Comp./yr. * 11yrs. = 44 Compounding periods.

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  2. d. P = Po*e^rt.
    P/Po = e^rt.
    r*t = 0.045/yr. * 11yrs. = 0.495,
    e^0.495 = P/Po,
    1.6305 = P/500, P = $820.25.

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