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EXAMPLES. (29) If a salary, payable yearly, amount to 16121. 10s. in 6

years, at 3 per cent. what is the salary? (30) The amount of a salary payable half-yearly, for 6

years, at 3 per cent. is 16231. 158. What is the salary? (31) If the amount of an annuity, payable quarterly, be

16291. 7s. Od. for 6 years, at 6 per cent, what is the annuity?

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

20- 2ut THEOREM 11.

R.

utt - ut

When the payments are half-yearly, take 4a-4ut for a dividend; if quarterly, take 8a-ut, and proceed with the annuity and time as is mentioned in theorem 9.

EXAMPLES (32) If a salary of 250l. per annum amount to 16121. 10s, in

6

years, what is the rate per cent. ? (33) If a salary of 250l. per annum, payable half-yearly,

amount to 1623l. in 6 years, what is the rate per

cent.? (34) Suppose a pension of 250l. per annum, payable quar

terly, amount to 1629). 7s. 6d. in 6 years, what is the rate per cent. ?

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Case 13. When U, A, and R are given, to find T. 2

2n

xxx THEOREM 12, First 1=X. Then

T.

4 *2 When the payments are half-yearly or quarterly, proceed with the ratio and annuity as mentioned before, and T will be equal to those half-yearly or quarterly payments.

EXAMPLES. (35) In what time will a salary of 250l. per annum amount to

16121. 10s. at 3 per cent. ? (36) If an annuity of 2501. per annum, payable half-yearly, amount to 16231. 155. at 3 per cent. what time were

the payments forbornę? (37) If an annuity of 250l. per annum, payable quarterly,

amount to 16291. 7s. 6d. at 3 per cent. what was the time of forbearance?

LXIII. PRESENT WORTH of ANNUITIES, &c. HERE P represents the present worth, U, T, and R, as before.

Case 14. When U, T, and R are given, to find P.
THEOREM 13.

th-tr+2+.

:x U =P.

2tr +2 The same is to be observed here for half-yearly and quare terly payments as before mentioned.

EXAMPLES. (38) What is the present worth of 2501. per annum, to con

tinue 6 years? (39) What is the pension of 250l. per annum worth in ready

moriey, payable half-yearly, at 3 per cent. for 6 years? (40) What is the present worth of 250l. payable quarterly,

for 6 years, at 3 per cent. ?

Case 15. When P, T, and R are given, to find 0.

trti THEOREM 14.

: x 2p=U.

tr-r+2 When the payments are half-yearly, multiply by ip; for quarterly, by sp; and proceed with t and r as before di rected.

EXAMPLES. (41) What annuity is that which, for 6 years' continuance,

produces 1366. 108. 6d. present worth, at 3 per cent. ? (42) There is an annuity, payable half-yearly, for 6 years to

come ; what is the yearly income, when the present worth, at 3 per cent. is 13761. 5s..

K

(43) There is an annuity, payable quarterly, for 6 years te

come; what is the yearly income, when the present worth is.13801. 17s. 6d. at 3 per cent. ?

Case 16. When U, P, and T are given, to find R.

ut-PX2 THEOREM 15.

: R.

2pt+ut - ult When the payments are half-yearly or quarterly, proceed with the annuity and time as before directed ; and the quotient will be the answer accordingly; i. e. if for half-yearly, the quotient will be half the ratio, and if for quarterly, a fourth part of the ratio.

EXAMPLES. (44) At what rate per cent. will an annuity of 2501. per

annum, to continue 6 years, produce the present worth

of 13661. 10s. 6d.? (45) If an annuity of 250l. per annum, payable half-yearly,

having 6 years to come, be sold for 13761. 5s. what is

the rate per cent.? (46) At what rate per cent. will an annuity of 250l. per

annum, payable quarterly, to continue 6 years, produce 13801. 175. 6d. for the present worth?

Case 17. When U, P, and R are giren, to find T.

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UT

4

2

2p Then

+ When the payments are half-yearly, or quarterly, proceed with the annuity and ratio as before directed, and the quotient will be the number of payments.

EXAMPLES. (47) If an annuity of 250l. per annum produce 13661. 10s. 6d.

for the present worth at 3 per cent., what is the time of its continuance?

(48) An annuity of 2501. per annum, payable half-yearly, is

sold for 13761. 55. at 3 per cent. I desire to know the

number of payments and time to come. (49) Suppose a lease of a house of 250l. per annum, payable

quarterly, be sold for 13801. 17s. 6d. at 3 per cent. I demand the number of payments, and time to come.

LXIV. ANNUITIES, &c. taken in REVERSION.

Case 18. To find the present worth of an amuily taken in Reversion. RULE.

THEOREM 17. 1. Find the present worth of

the yearly sum at the given tr-tr-2t rate, and for the time of its 1. Thus

:XU=P. continuance.

2tr42 2. Change Pinto A, and find

what principal being put to
interest will amount to A | 2. Thus P.
at the same rate, and for

tr +
the time to come, before
the annuity, &c. com-

mences.

EXAMPLES (50) What is the present worth of 2501. per annum, to con

tinue 6 years, but not to commence until the end of

4 years, ailowing 3 per cent to the purchaser ? (51) What is the present worth of a lease of 80l. per an

num, to continue 7 years, but not to commence until the end of 5 years, allowing 41 per cent, to the pur

chaser? (52) There is a legacy of 40l. per annum, for 10 years,

left to a person of 14 years of age; the time of payment is not to commence till the said person's age be 21; but he, wanting a sum of money, is inclined to sell the same at 5 per cent. I demand the present worth.

Case 19. To find the yearly income of an annuity, &c. in reversion.

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EXAMPLES. (53) A person having an annuity left him for 6 years and 5

months, but not to commence till the end of 4 years, has disposed of it for the present payment of 12201. 2s. 2d. allowing 3 per cent to the purchaser. What is

the yearly income? (54) There is a lease of a house taken for 7 years, but not

to commence until the end of 5 years: the lessee would sell the same for 4191. 15s. 11d. present payment, allowing 41 per cent, to the purchaser. What

is the yearly rent? (55) There is a legacy of a certain rate per annum, for 10

years, left to a person of 14 years of age; but the time of payment is not to commence till the said person's age be 21 years; but he, wanting a sum of money, sold it for 2411. 19s. 6d. allowing 5 per cent. to the buyer. I demand the yearly rate.

I.XV. REBATE or DISCOUNT. HERE S represents the sum to be discounted, P the present worth, T and R as before.

Casé 20. When S, T, and R are given, to find P.

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(56) What is the present worth of 1501. due 9 months hense,

at 5 per cent. ?

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