3. If the yearly rent of a house, being forborne 7 years at 6 per cent, amounts to £335 15s. old. what is the rent per annum? Ans. £40.

4. If the payment of a falary be omitted 6 years; how much is the falary when the amount is £241 1. 73d. at 5 per

cent?

Ans. £35. 5. What annuity, payable half yearly, will amount to £111 12. 6d. in years, at 5 per cent? Ans. £10.

The annuity, amount, and rate of interest given, to find the time. RULE.-Multiply the amount by the ratio lefs 1, divide the product by the annuity, and add an unit to the quotient; then involve the ratio up to the fum, and the power to which it is raised will indicate the time; or,

Find the faid fum in Table I. under the rate, and against it in the column of the years, will be the time required.

NOTE. If the sum be not an even yearly power, work as the Note in page 190 directs.

Examples.

1. In what time will £30 per annum amount to £129 6f. 1d. allowing compound intereft at 5 per cent?

Ans. 4 years.

05

£129. 6 1 = 129.30416

Ratio 1.95 1 =

Annuity 3.0)6.4652080

Quotient X 1= 1.21550693; then

1.c5 X 1.05 X 1.05 1.05 = 1.21550625

the 4th power of the ratio, indicating 4 years, for the answer.

2. In what time will a penfion of £50 per annum amount to £270 16s. 4d. at 4 per cent? Ans. 5 ears. 3. In what time will the yearly rent of a houfe, at £40 per annum, amount to £335 15 d. at 6 per cent for non payment? Ans. 7 years. 4. In what time will a falary of £35 per annum, amount to £241 15. 7 d. at 5 per cent? Ans. 6 years.

The annuity, time, and rate given, to find the present worth.

RULE. Divide the annuity by the ratio involved to the time, and subtract the quotient from the annuity; divide the remainder by the ratio lefs one, and the quotient will be the present worth; or,

By TABLE IV.

Multiply the number under the rate, and oppofite the time by the annuity, and the product will be the prefent worth.

When the payments are half yearly or quarterly, multiply the prefent worth fo found, by the proper number in Table V.

Examples.

1. What is the prefent worth of 20l. a year for 6 years, pay able either yearly, half yearly, or quarterly, computing at per cent per annum?

Or, by Table IV. 5.07569 20 101.51387.the prefent worth for yearly payments: Then by Table V.

1.012348

=

102.7673, for half yearly. 1.018559 £103.3978, for quarterly.

2. What is the prefent worth of an annuity of 30l. per annum to continue 5 years, at 4 per cent? Ans. £133 11s. 1d. 3. What ready money will purchase an annuity of £50, to continue 4 years, at 6 per cent? Ans. 173 5. Id.

4. If the yearly rent of an estate be 70l. what will purchafe it for 4 years at 51 per cent? Ans. 2451. 75. 2 d.

The present worth, time and ratio given, to find the annuity.

RULE.-Maltiply the ratio involved to the time, the ratio lefs one, and the prefent worth together for a dividend, take an unit from the ratio involved to the time for a divifor, the quotient will be the annuity; or, by

TABLE IV.

Divide the prefent worth by the number for the rate and time, and the quotient will be the annuity.

When the payments are half yearly or quarterly, divide the annuity fo found by the proper number in Table V.

Examples.

1. What annuity, payable yearly, half yearly, or quarterly, for 6 years, may be purchafed for 1017. 10s. 314. at 5 per cent per annum, Compound Interest?

2. What annuity for 5 years, will 1337. 118. 1d. prefent money, purchase at 4 per cent?

Ans. 301. 3. Suppofe the leafe of a houfe for 4 years be fold for 245/ 75. 2 d. what is the yearly rent, allowing 5% p. ct. Ans. 7ol.

The anuuity, present worth, and ratio given, to find the time.

RULE. Multiply the present worth by the ratio lefs one, subtract the product from the annuity, and divide the annuity by the remainder; then involve the ratio till it equals (or nearly equals) the quotient, and the power to which it is raised will indicate the time; or, find the quotient in Table II. un der the rate, and against it, in the left column, ftands the time.

Examples.

1. How long may a leafe of 201, yearly rent, be poffeffed for 2017. 10. 3 d. down, allowing 5 per cent per annum to the purchafer?

14 924274/20.000000(1.34009 og indicating 6 years

for the answer.

198 ANNUITIES, &c. TAKEN IN REVERSION.

2. For what time will 133. 11. 1d. purchase a leafe of 30% a year at the rate of 4 per cent? Ans. 5 years. 3. If 1734. 55. 1 d. be paid down for a lease of 50l. per annum, at 6 per cent, for what time is the purchase made? Ans. 4 years,

4. If an eftate be let for 70l. per annum, and the lefsee make present payment of 2451. 75. 2 d. at 5 what term is the leafe purchased?

Annuities, &c. in Reversion,

per cent, for Anf. 4 years.

The annuity, time of reversion, time of continuance, aud ratio given, to find the present worth.

RULE.-Divide the annuity by the ratio involved to the time of continuance, and fubtract the quotient from the annuity for a dividend; multiply the ratio involved to the time of reverfion by the ratio lefs one for a divifor; the quotient of this divifion will be the present worth.

Or, take two numbers under the given rate in Table IV. viz: That oppofite the fum of the two given times, and that against the time of reverfion, and multiply their difference by the annuity for the prefent worth.

When the payments are half yearly or quarterly, multiply the prefent worth, by the proper number in Table V.

Examples.

1. What is the prefent worth of a lease of 201. per annum, to continue 4 years, but not to commence till the end of two years, allowing 5 per cent to the purchaser ?

1.05 X .05=

.055125)3.54595(64.326 Answer,

From Table IV. for {9 years=

6 years 5.07569.
2 do.

=

1.85941

3.21628

20

Answer 64.32560 as before.

2. What is the present worth of 32% per annum to continue

7 years, but not to commence till 4 years

per cent to the purchaser?

hence, allowing 5 Ans. 1521. 6. 81d.

ANNUITIES, &c. TAKEN IN REVERSION. 199

3. A tenement which is now building, is proposed to be let for 8 years, at 100l. per annum, but cannot be finifhed till the end of 2 years; what is the prefent worth of fuch a leafe, allowing 4 per cent for prefent payment? Anf. 6221. 95. 72d.

The present worth, times, and ratio given, to find the annuity.

RULE.-Involve the ratio to the years from the time of purchafe to the expiration of the annuity for a dividend, and from the ratio involved to the time of continuance take one for a divifor, the quotient multiplied by the present worth and the ratio lefs one gives the annuity. Or,

Take two numbers from table IV. as in the rule preceding, and divide the present worth by their difference.

When the payments are half yearly, or quarterly, divide the annuity by the proper number in Table V.

Examples.

1. What annuity or yearly rent, to be entered upon 2 years hence, and then to continue 4 years, may be purchased for 644 6s. 6d. ready money, at 5 per cent?

Answer. £20,00005

from Table IV. f5.07569 for 6 years.

1.85941 for 2 years.

Difference 3.21628(64.326(20%. Answer.

2. The prefent payment for the leafe of a house is 6221. gs. 74d. the leafe to commence two years hence, and to continue eight years; how much is the yearly rent, when 4 per cent is allowed for prefent money? Ans. £100.

The present worth, annuity, rate of interest, and time of reversion given, to find the time of continuance.

RULE.-Subtract the continued product of the ratio involv ed to the time of reverfion, the ratio lefs one and the present worth from the annuity, and divide the annuity by the remain-, der: Then involve the ratio till it (nearly) equals the quotient, and the power will indicate the time required. Or,

Find the faid quotient in Table II. under the rate, and against it ftands the time.