§ Mr. NEWMANasked what would be the length of the term during which, under normal conditions, a purchase annuity would be payable by the tenant-purchaser if the interest were 3 per cent. throughout the whole term, and the sinking fund were ½ per cent. for the first ten years, ⅜per cent. for the second ten years, and a ¼ per cent. for the residue of the term; if the interest were 3 per cent. during the whole term, and the annuity were 3½ per cent. for the first ten years, what would be, under normal conditions, the unpaid or 1610W outstanding amount of an advance of £100 at the end of the first ten years; what would be the annuity at 3½ per cent. on that amount for the second ten years; what, would be the unpaid or outstanding amount of the original advance of £100 at the end of the second ten years; what would be the annuity at 3½ per cent. on that amount for the residue of the term necessary for the repayment of the residue of the advance; and what would be the length of the period during which the last-named annuity should be paid?

§ Mr. ILLINGWORTHThe term of the annuity referred to in the first part of the question would be seventy-six years. The 3½ per cent. annuity to replace £100 with interest at 3 per cent., and subject to two decadal revisions, would be £3 10s. for the first ten years, £3 6s. for the second ten years, and £3 2s. 2d. for the succeeding 65½ years. The capital outstanding at the end of the first decade would be £94 4s. 5d., and at the end of the second decade £88 15s. 6d.