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Case 9. When U, R, and T, are given, to find P.

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By Table V. thus: Multiply the tabular Number for the given Time and Rate by the Annuity, &c. the Product will be the present Worth required.

EXAMPLES.

(27) What is the present Worth of an Annuity of 50! per Annum, to continue 8 Years, at 5 per Cent.?

(28) What is the present Worth of an Annuity or Yearly Rent of 60%. to continue 6 Years, at 4 per Cent.? (29) What is the present Worth of a Pension of 1000/ per Annum, for 21 Years, at 4 per Cent.?

Case 10. When P, T and R, are given, to find W.

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By Table V. thus: Divide the present Worth by the fabular Nursber for the given Time and Rate; and the Quotient will be the Annuity required.

Or by Table VI. thus: Multiply the tabular Number (for the given Rate and Time) by the present Worth; and the Product will be the Annuity.

EXAMPLES..

(30) If the present Worth of 3231 3s 24d were required for a Pension of 8 Years to come, at 5 per Cent. what was the Pension ?

(31) What Annuity or Yearly Rent may be purchased for 314/ 10s 64d at 4 per Cent. for 6 Years?

(32) Suppose the present Worth of a Pension for 21 Years, at 4 per Cent, was 13404/ 14s 54d. what was the

Pension?

Case 11. When U, P, and R, are given, to find T.

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By Table V. thus: Divide the present Worth by the Annuity, and the Quotient will be the Amount of 17 at the given Rate, which will be found under the said Rate, even with the Time required.

EXAMPLES.

(33) How long may one have a Lease of 501 Yearly Rent for 3231 3s 24d. allowing 5 per Cent. to the Pur

chaser?

(34) If an Annuity of 60/ is purchased for 3141 10s 63d at 4 per Cent. what Time ought it to continue? (35) I demand what Time a Lease of 1000/ may be purchased for, when the present Worth of 134047 14s 53d is made at 4 per Cent.?

Case 12. When U, P, and T, are given, to find R.

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This being a very high Equation, requires the Assistance of Algebra to determine R.

By Table V. Proceed as in the last Rule; and the Quetient will be the Amount of 1/ Annuity for the given Time, over which will be the Rate required.

EXAMPLES.

pur

(36) If an Annuity of 50l. to continue for 8 Years, be chased for 3251 3s 24d what Rate of Interest hath the Purchaser for his Money?

(37 Suppose I give 314/ 10s 63d for an Annuity of 60/ to continue 6 Years, at what Rate was interest allowed?

(38).

anuity of 1000l. to continue 21 Years, be purchased for 13404/ 14s 5d. what Rate of Interest is the Purchaser allowed for his Money?

LXX. ANNUITIES, LEASES, &c. taken in RE

VERSION.

To find the present Worth of Annuities, &c. in Reversion.

RULE.

1. Find the present Worth of the Anunity, &c. at the given Rate, and U for the Time of its Continuance, by Theorem 9.

Thus, THEO 15.

u

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A

Rt

2. Change P into A; and find what
Principal being put to Interest will
amount to P, at the same Rate and Thus-P.
Time to come before the Annuity
commences, by Theorem 2, which!
will give the present Worth of the
Annuity.

By Table V. thus: Find the present Value of 11.per Annum, at the given Rate, both for the Time being, and also for that and the Time in Reversion added together; then subtract the Time in being from the other, and multiply the Remainder by the Annuity; the Product will be the present Worth required.

EXAMPLES.

(39) What is the present Worth of a Reversion of a Lease of 80 per Annum, to continue 6 Years, but not to commence till the End of 2 Years, allowing 5 per Cent. to the Purchaser ?

(40) What ought a Person to give down in ready Money for the Reversion of 1000/ a Year, to continue 20 Years, on a Lease which cannot commence till 5 Years are at End, allowing the Purchaser 5 per Cent.? To find the Yearly Income of an Annuity taken in Rever

sion.

RULE.

1. Find the Amount of the

present Worth at the given

THEOREM 14.

Rate, and for the Time Thus, pri...A.

before the Annuity com

mences, by Theorem 1.

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By Table V. thus: Proceed as in the last Rule, and divide the present Worth by the Remainder: the Quotient will be the Annuity required.

EXAMPLES.

(41) What Annuity, to be entered upon two Years hence, and then to continue 6 Years, may be purchased for 368/ 6s Id ready Money, allowing 5 per Cent. to the Purchaser ?

(42) Suppose the present Worth of a Lease of an Estate is 8132/ 14s 8d. taken in Reversion for 20 Years, but not to commence till the End of 5 Years, allowing 5 per Cent. to the Purchaser: what is the Yearly Rent?

LXXI. REBATE or DISCOUNT.

Here S represents the Sum to be purchased.

When S, T, and R, are given, to find P.

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By the 4th Table, thus: Multiply the tabular Number for the given Time and Rate, by the Sum to be purchased; the Product will be the present Worth.

EXAMPLE.

(43) What is the present Worth of 1501. payable 4 Years hence, at 5 per Cent?

(44) What is the present Worth of 7431 4s 9d. payable 6 Years hence, at 4 per Cent.?

When P, T, and R, are given, to find S.

THEOREM 17. p × rt = S.

U

By Table IV. thus: Divide the present Worth by the tabular Number for the given Time and Rate; and the Quotient will be the Sum to be purchased.

EXAMPLES.

(45) If 123/ 8s 13d be received for a Debt payable 4 Years hence, and an Allowance of 5 per Cent. to the Debtor. for the present Payment, what was the Debt?

(46) If a Sum of Money, due 6 Years hence, produce 587/ 7s 93d for the present Payment, Rebate being made at 4 per Cent. I demand how much the Debt was?

When S, P, and R, are given, to find T.

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By Table IV. thus: Divide the Principal by the Sum to be purchased; and the Quotient will be the present Worth of 11 at the given Rate, which will be found under the Rate, and even with the Time required.

EXAMPLES.

(47) A Person received 123/ 8s 14d. for a Debt of 150%. Rebate being made at 5 per Cent. I demand in what Time the Debt was payable?

(48) The present Payment of 587/ 7s 9 d. is made for a Debt of 7431 4s 9d. Rebate at 4 per Cent. I demand when the Debt was payable ?

When S, P, and T, are given, to find R.

S

THEOREM 19.

Rt.

Which proceed with as in Theo

rem 4.

By Table IV. thus: Proceed as in the last Rule, and the Quotient will be the present Worth of 1 for the given Tire, which will be found even with the Time, and under the Rate required.

EXAMPLES.

(49) The present Worth of 150l. payable 4 Years hence, is 1231 8s 1d. At what Rate per Cent. is the Rebate

made?

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