forbear_v be_v 3_o 34978._o and_o the_o interest_n of_o one_o pound_n for_o a_o quarter_n be_v 0_o 14675_o wherefore_o by_o proportion_n as_o 014675_o be_v to_o 2_o 34978_o so_o be_v 25_o to_o 4003_o 032_o that_o be_v 4003_o l._n 00_o s._n 7¾_n d._n this_o useful_a proportion_n i_o thus_o demonstrate_v which_o the_o reader_n may_v pass_v by_o imagine_v the_o land_n or_o stock_n that_o yield_v a_o annuity_n to_o be_v such_o a_o principal_n send_v out_o for_o the_o whole_a term_n as_o will_v bring_v in_o so_o much_o yearly_a interest_n as_o the_o annuity_n come_v to_o then_o at_o last_o the_o whole_a at_o compound_v interest_n be_v to_o be_v repay_v whereof_o so_o much_o be_v suppose_v to_o be_v repay_v in_o the_o value_n of_o the_o land_n as_o its_o first_o principal_a come_v to_o and_o the_o rest_n in_o money_n wherefore_o out_o of_o the_o whole_a amount_v of_o that_o principal_a and_o its_o interest_n the_o principal_a must_v be_v deduct_v unless_o to_o shun_v it_o by_o that_o which_o geometer_n call_v conversion_n see_v commentator_n on_o 16_o def._n quinti_fw-la euclidis_fw-la etc._n etc._n we_o say_v as_o the_o first_o term_n be_v to_o the_o difference_n of_o the_o first_o and_o second_o so_o the_o three_o term_n to_o the_o difference_n of_o the_o three_o and_o four_o the_o plain_a proportion_n ground_v upon_o the_o former_a consideration_n run_v thus_o as_o 1_o l._n principal_n be_v to_o its_o amount_v for_o the_o time_n forbear_v so_o the_o principal_a that_o shall_v bring_v in_o any_o annuity_n propose_v to_o the_o sum_n of_o the_o say_v principal_a and_o of_o the_o arrearage_n of_o the_o annuity_n then_o it_o will_v hold_v by_o conversion_n of_o reason_n as_o 1_o l._n forbear_v at_o compound_v interest_n be_v to_o its_o amount_v less_o by_o a_o unit_fw-la for_o the_o time_n forbear_v so_o be_v the_o principal_a of_o a_o annuity_n forbear_v the_o like_a time_n to_o the_o arrearage_n of_o the_o annuity_n and_o instead_o of_o the_o three_o term_n of_o this_o proportion_n we_o may_v take_v in_o a_o fraction_n equivalent_a thereto_o the_o numerator_n whereof_o be_v the_o annuity_n or_o yearly_a payment_n of_o rent_n and_o the_o denominator_fw-la the_o interest_n of_o 1_o l._n for_o a_o year_n for_o to_o find_v the_o principal_a of_o a_o annuity_n say_v as_o 6_o be_v to_o 100_o or_o rather_o 06_o 1._o so_o be_v the_o annuity_n to_o its_o principal_n and_o both_o these_o latter_a proportion_n compound_v into_o one_o will_v be_v the_o proportion_n first_o deliver_v the_o unit_v in_o each_o be_v expunge_v as_o insignificant_a either_o in_o multiplication_n or_o division_n prop._n 5._o to_o find_v the_o present_a worth_n of_o a_o annuity_n if_o a_o annuity_n be_v forbear_v till_o the_o last_o payment_n be_v due_a then_o for_o as_o much_o as_o the_o interest_n of_o each_o particular_a payment_n be_v by_o the_o former_a or_o four_o proposition_n compute_v if_o by_o the_o 3d._a proportion_n the_o same_o together_o with_o the_o rebate_v of_o each_o payment_n be_v destroy_v to_o wit_n the_o present_a worth_n of_o the_o whole_a arrearage_n be_v compute_v it_o shall_v be_v the_o present_a worth_n of_o the_o annuity_n the_o proportion_n in_o both_o those_o proposition_n be_v after_o the_o manner_n of_o the_o four_o prop._n compose_v into_o one_o it_o will_v hold_v for_o annual_a payment_n at_o 6_o per_fw-la centum_fw-la as_o the_o fact_n of_o ,06_o the_o interest_n of_o 1_o l._n for_o a_o year_n and_o of_o the_o amount_v of_o one_o pound_n compound_v interest_n for_o the_o time_n propose_v be_v to_o the_o say_v amount_v less_o an_o unit._n so_o be_v the_o annuity_n or_o yearly_a rent_n to_o the_o present_a worth_n thereof_o example_n first_o for_o make_v the_o table_n to_o find_v the_o present_a worth_n of_o a_o annuity_n of_o 1_o l._n per_fw-la annum_fw-la to_o continue_v 25_o year_n at_o 6_o per_fw-la centum_fw-la compound_v interest_n the_o amount_v of_o 1_o l._n for_o that_o time_n be_v 4,29187_o which_o multiply_v by_o ,06_o the_o fact_n be_v ,257512_o whereby_o divide_v 3,29187_o the_o quote_v be_v 12_o l._n ,78335_o the_o present_a worth_n seek_v example_n second_o for_o half-year_o payment_n a_o annuity_n of_o 40_o l._n payable_a 20_o l._n each_o half_a year_n be_v to_o befold_a for_o 12_o year_n at_o 6_o per_fw-la centum_fw-la the_o compound_v inter_v of_o 1_o l._n for_o half_a a_o year_n be_v ,029564_o the_o amount_v of_o 1_o l._n forbear_v 12_o year_n 2,012196_o multiply_v these_o two_o together_o and_o that_o add_v together_o make_v the_o fact_n of_o both_o which_o be_v ,058487_o it_o therefore_o hold_v as_o ,058487_o be_v to_o ,1,012196_o so_o be_v 20_o to_o 346_o 166_o that_o be_v 346_o l._n 3_o s._n 4_o d._n the_o present_a worth_n thereof_o if_o this_o annuity_n be_v pay_v yearly_a it_o must_v be_v of_o less_o value_n because_o the_o money_n be_v long_o in_o come_v in_o and_o according_o the_o worth_n of_o it_o l._n s._n d._n will_v be_v but_o 335_o 7_o 1_o admit_v it_o be_v require_v to_o know_v what_o a_o addition_n of_o 8_o year_n more_o be_v worth_a after_o 12_o be_v expire_v  _fw-fr the_o worth_n of_o the_o say_a annuity_n for_o 20_o year_n be_v 458._o 15._o 11_o the_o difference_n of_o these_o two_o be_v be_v the_o present_a worth_n of_o the_o 8_o year_n seek_v 123._o 8._o 10_o prop._n 6._o to_o find_v what_o annuity_n any_o sum_n of_o ready_a money_n shall_v purchase_v this_o be_v but_o the_o converse_n of_o the_o former_a proposition_n and_o it_o hold_v therefore_o as_o the_o amount_v of_o 1_o l._n forbear_v at_o compound_v interest_n less_o an_o unit_fw-la be_v to_o the_o fact_n of_o 06_o and_o of_o the_o amount_v of_o one_o pound_n so_o forbear_v so_o be_v any_o sum_n of_o ready_a money_n to_o the_o annuity_n it_o shall_v purchase_v in_o this_o and_o the_o two_o former_a proposition_n by_o ,06_o be_v understand_v the_o compound_v interest_n of_o 1_o l._n for_o a_o year_n and_o when_o the_o payment_n be_v by_o quarter_n or_o half_a year_n instead_o thereof_o must_v be_v put_v in_o the_o interest_n of_o a_o quarter_n or_o half_a a_o year_n and_o instead_o of_o the_o annuity_n or_o yearly_a payment_n the_o quarterly_o or_o half-year_o payment_n according_o corollary_n if_o 1_o l._n be_v the_o sum_n of_o ready_a money_n than_o the_o two_o middle_a term_n of_o the_o proportion_n be_v the_o fact_n above_o mention_v and_o you_o will_v frame_v the_o other_o vulgar_a table_n for_o this_o purpose_n example_n the_o first_o to_o find_v what_o annuity_n 1_o l._n shall_v purchase_v to_o continue_v 30_o year_n it_o hold_v as_o 4,74349_o to_o ,06_o so_o 5,74349_o to_o 0,07264_o example_n second_o let_v it_o be_v require_v to_o find_v what_o rend_v payable_a yearly_a 8_o l._n shall_v purchase_v at_o 6_o per_fw-la centum_fw-la to_o continue_v 21_o year_n as_o 2,39956_o the_o amount_v less_o an_o unit_fw-la of_o 1_o l._n for_o 21_o year_n be_v to_o ,20397_o the_o fact_n of_o ,06_o and_o the_o amount_v so_o be_v 8_o to_o ,68_o or_o 13_o s._n 7¼_n d._n the_o annuity_n seek_v memorandum_n that_o by_o the_o fact_n be_v mean_v that_o you_o shall_v multiply_v the_o forego_n figure_n by_o ,06_o viz._n 2,39956_o by_o ,06_o which_o make_v 2,2039736_o now_o whereas_o the_o lease_n of_o a_o house_n of_o 1_o l._n per_fw-la annum_fw-la to_o continue_v 21_o year_n be_v common_o sell_v for_o 8_o l._n or_o 8_o year_n purchase_n and_o your_o money_n will_v purchase_v a_o certainty_n but_o of_o 13_o s._n 7_o d._n â—_o per_fw-la annum_fw-la you_o see_v by_o this_o supposition_n you_o be_v abate_v 6_o s._n 5_o d._n 3_o â—nt_fw-la of_o tax_n reparation_n and_o casualty_n and_o verygood_a reason_n there_o be_v for_o great_a abatement_n for_o a_o tenant_n take_v a_o lease_n on_o a_o tunber_n house_n if_o it_o be_v burn_v down_o by_o a_o fire_n beginning_n at_o his_o neighbour_n as_o lease_n common_o run_v be_v bind_v to_o build_v it_o up_o again_o and_o have_v no_o relief_n either_o in_o law_n or_o equity_n against_o his_o landlord_n as_o i_o be_o inform_v by_o able_a council_n only_o he_o have_v the_o benefit_n of_o a_o benevolence_n his_o action_n against_o they_o where_o the_o fire_n begin_v who_o perchance_o be_v ruin_v s._n  _fw-fr s._n d._n  _fw-fr will_v purchase_v a_o 11_o 11_o 10_o annuity_n to_o continue_v 21_o year_n of_o 12_o 9_o 10_o  _fw-fr 14_o 5½_n  _fw-fr  _fw-fr 15_o  _fw-fr  _fw-fr 17_o  _fw-fr  _fw-fr 1_o 5_o 3½_n 1-00-0_a hence_o it_o appear_v that_o the_o value_n of_o lease_n of_o house_n can_v be_v estimate_v near_o the_o truth_n by_o the_o common_a table_n for_o annuity_n at_o the_o currant_n rate_n of_o interest_n and_o that_o if_o any_o one_o will_v use_v they_o to_o this_o purpose_n it_o be_v much_o near_o the_o truth_n first_o to_o abridge_v the_o rent_n as_o