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A deferred annuity on (40) provides for an income of 1000 per year for life beginning at age 60. If (40) lives to age 60, the first 10 annuity payments are guaranteed regardless of whether (40) is alive or not. Level annual premiums of P are payable for 10 years, beginning at age 40. If (40) dies before the annuity begins, all premiums paid prior to death are returned at the end of the year of death, and no annuity payments are made. Find a formula for P, assuming: (a) premiums are returned without interest; (b) premiums are returned with interest.

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