Ty received a separation payment of $25 000 from his former employer when he was 35-years old. He invested that sum of money at 5.5% compounded semi-annually. When he was 65, he converted the balance into an ordinary annuity paying $6000 every 3 months with interest at 6% compounded quarterly. For how long will the annuity continue to pay him?

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  1. the value of i for the first investment = .055/2 = .0275
    amount of his investment after 30 years = 25000(1.0275^60) = $127,306.28 , nice!
    This becomes the present value of an annuity for n quarter years, ....
    the quarterly interest rate is .06/4 = .015
    6000( 1 - 1.015^-n)/.015 = 127306.28
    1 - 1.015^-n = .3182657
    -1.015^-n = -.6817343
    1.015^-n = .6817343
    take log of both sides, and apply log rules
    -n log 1.015 = log .6817343
    -n = -25.73
    n = 25.73 <---- quarter years or 6.4 years

    Hope Ty has other sources of income in his retirement.

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  2. Reiny's incorrect, mm! Don't trust that person, I don't even know if it's a boy or a a girl, but she's WRONG!

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  3. aa

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