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1. An annuity on (x) and (y) provides yearly payments as long as either (x) or (y) are alive. Payments begin at 12, but reduce to 8 if (x) only is alive or to (6) if (y) only is alive. Find the present value.

2. A temporary life annuity on (y) provides for payments made continuously at the annual rate of 1 for n years, but with the payments beginning at the death of (x), rather than at time 0. Payments stop at the death of (y). Find a formula for the present value.

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