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ANNU-T-1Es un PENSIONs. 103

3. Seven gentlemen met at an inn, and were so well pleased with their host, and with each other, that they agreed to tarry so long as they, together with their host, could sit every day in a different position at dinner; how long must they have staid at said inn to have fulfilled their agreement? Ans. 110}o years.

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CASE I. Te find the amount of an Annuity, or Pension, in arrears, at Compound Interest.

RULE.

1. Make 1 the first term of a geometrical progression, and the amount of $1 or £1 for one year, at the given rate per cent, the ratio.

2. Carry on the series up to as many terms as the given number of years, and find its sum.

3. Multiply the sum thus found, by the given annuity, and the product will be the amount sought.

Ex-MPLEs.

1. If 125 dols. yearly rent, or annuity, be forborne (or anpaid)4 years; what will it amount to at 6 per cent. per annum, compound interest?

1+1,06+1,1236+1,191016–4,374616, sum of the series.” Then, 4,374616X 125–$546,827, the amount sought.

OR BY TABLE II. Multiply the Tabular number under the rate, and opposite to the time, by the annuity, and the product will be the amount sought.

* The sum of the seriesthus found, is the amount of 11...or 1 dollar ano for the given time, which may be found in Table II. ready calcula

ñense, either the amount or present worth of annuities may be readih sound by ta-les for that purpose.

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The sum, =6 years, gives 5,075692
Time in reversion, –2 years, 1,859.410

Remaintler, 3,216282x50 Ans. E160,8141. 2. What is the present worth of 75l. yearly rent, which is not to commence until 10 years hence, and then to continue 7 years after that time at 6 per cent.” Ans. E233 15s. 9d. 1. What is the present worth of the reversion of a lease of 60 dollars per annum, to continue 20 years, but not to commence till the end of 8 years, allowing 6 per cent to the purchaser? Ans. $431, 78cts. 2 om. IV. To find the present worth of a Freehold Estate, or a Annuity to continue forever, at Compound Interest. RULE. As the rate per cent, is to 100l. : so is the yearly rent to the value required.

Ex-MPLEs. 1. What is the worth of a freehold estate of 401 per an num, allowing 5 per cent to the purchaser?

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2. An estate brings in yearly 150l. what would it sell for

allowing the purchaser 6 per cent for his money? Ans. E2500. W. To find the present worth of a Freehold Estate, in Reversion, at Compound Interest. Rule.-1. Find the present value of the estate (by the foregoing

rule) as though it were to be entered on immediately, and divide the said value by that power of the ratio denoted by the time of rever. sion. and the quotient will be the present worth of the estate in re-------

Ex-MPLEs. 1. Suppose a freehold estate of 401 per annum to com mence two years hence, he put on sale; what is its value, allowing the purchaser 51 per cent.”

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