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and allow him 5 per cent for present payment; I demand how much the debt is? Ans. 161l 10s.

3 A legacy was left me the 24th of July, 1798, to be paid on the Christinas-Day following, but I agree with the Exeeutor, and allow bim 6 per eent for the present payment of 9751 3s 0d 3 qrs. I demand what the Legacy was ? Ans. 1000l.

OASE 3. Q. When S, P, and R, are given to find: T, how is it discovered?

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EXAMPLES * The present worth of 7951 11s 2d due fór a certain time to come, is 7541 18.8d at 6 per cent. I demand in what time the first sum should have been paid, if no rebate had been made? Ans. 11 months.

2 There is 1611 :Os due at a certain time to come, but I allow 5 per cent to the debtor, for the present payment of 1491 133 01 3 qrs. I demand when the sum should have been paid without any rebate ? Ans. 19 months.

3 I have received 975l 38 od 3 qrs. for a legacy of 1000l. allowing the executors 6 per cent. I demand when the legacy was payable without rebate ? Ans. 155 days.

CASE 4. Q. When S, P, and T, are given to find R, how is it discovered ?

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1 At what rate per cent will 7951 11s 2d payable 11 months hence produce 7451 is 8d for the present payment? Ans. 6 per cent.

2 At what rate per cent will 1611 10s payable 19 months hence, produce the present payment of 1491 135 0d 3 qrs.? Ans. 5 per cent.

3 Suppose a legacy of 10002 is left me the 24th of July, 1798, to be paid on the Christmas-day following, but I agree with the executor for the present payment of 9751

I demand the rate per cent allowed for his money? Ans, 6 per cento

85 od 3 qrs

OF EQUATION OF PAYMENTS.

(THE TRUE WAY.) Q. How is the equated time for the payment of a sum of money due at several times, found out?

A. Thus; 1. find the present worth of each payment for its respective time, as in Rebate, that is;

S

EXAMPLES.

t=1. 2 Add all the present worths together, and call that sum also P; then is smp=d the Rebate,

d 3

=e is the true equated time.

pr 1 A owes B 2001 to be paid as follows, viz. 1'ool at 8 months; and 100l at 4 months: but they agree to have but one payment of the whole, Rebate being made at 6 per cent. I demand the true equated time? Ans. 3 months.

2 A Merchant hath owing him 3001 to be paid as follows; 501 at 2 months, 1001 at 5 months, and the rest at 8 months; and it is agreed to have but one payment of the whole, Rebate being made at 5 per cent. I demand the equated time? Ans. 5.9796 months.

3 F owes to H 1000l whereof 2001 is to be paid present; 4001 at 5 months; and the rest at 10 months; but they agree to have but one payment of the whole, at the rate of 3 per cent Rebate; I demand the true equated time? Ang. 181 days.

4 A man owes a merchant 1200l to be paid as follows-> 2001 down, 5001 at the end of 10 months; and the rest at the end of 20 months; and they agree to have but one

payment of the whole, Rebate at 8 per cent. I demand the true equated time? Ans. 1 year, 11 days.

OF COMPOUND INTEREST.

Q. W

HAT particular Letters are used here?
4. These:
P, the Principal.
T, the Time;
R, the amount of 11 for 1 year at any given Rate;
A, the whole amount.

Q. How is the amount of 11 for 1 year, at any propora ed rate per cent found?

7 /

A. Thus: As 100 : 106 :: 1 : 1.06

100 : 105 :: 1 : 1.05, &c. A Table of the Amounts of 1l for 1 Year. Rates per C1.Amts. of 11.Rates per Ct. Amts. ofl. 2 1.02 6

1.65
3
1.03
7

1.07
31
1.035

1.075
1.04
8

1.08
44
1.045
84

1.085
5
1.05
9

1.09
51
1.055

1.095
6
1.06
10

1.1 CASE 1. Q. When P. T, and R, are given to find' A, how is it discovered?

t A. Thus: pxr=d. Note, R must be involved so many times as the number of

t direct, and that will be r.

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EXAMPLES.

1 What sum will 450l amount to in 3 years time, at 5 per cent per ann.? Answer 5201 188 7d 2 qrs.

2 What will 4001 amount to in four years at 6 per cent. per ann,? Answer 5041 19s 9d 3.15264 qrs.

3 What will 4801 amount to in 6 years, at 5 per cent: per ann.? Answer 6431 4s 41.0178d.

4 What is the amount of 500l at 41 per cent per ann. for 4 years ? Answer 5901 11s 5d 2.954 qrs.

CASE 2. Q. When A, R, and T, are given to find P, how is it discovered?

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i What principal must be put to interest to amount to the sum of 5201 18s 7d 2 qrs. in 3 years, at 5 per cent. per ann. ? Answer 4501.

2 What principal will amount to 5041 198 9d 3.15264 qrs. in 4 years, at 6 per cent. per ann.? Answer 4001.

3 What principal will amount to 6431 4s 11.0178d in 6 years, at 5 per cent. per ann. ? Answer 4801.

4 Wlat principal will amount to 5901 11s 5d 3qrs in 4 years, at 44 per cent ? Ans. 500l.

CASE 3. Q. When P, R, and A, are given to find T, how is it discovered ?

1) which being continually divided by

r, till nothing remains, the NumP

ber of those divisions will be=t.

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A. Thus ;

EXAMPLES

1 In what time will 4501 amount to 5201 18s 7d 2qrs at 5 per cent. per ann? Ans. 3 years.

2 In what time will 4001 amount to 5041 19s 9d 3.2qrs. at 6 per cent. per ann? Auswer 4 years.

3 In what time will 4801 amount to 6431 145 11.id at 5 per cent per ann? Answer 6 years.

4 In what time will 500l amount to 5901 11s 5d 3ers. at 44 per cent per ann? Ans. 4 years.

CASE 4.

Q. When P, A, and T, are given to find R, low is it discovered?

which must be extracted by the

rules of extraction ; the time givA. Thus ;

en in the question=t shewing the P

power.

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t

EXAMPLES.

1 At what rate per cent will 4501 amount to 5201 18s 7d 2qrs in 3 years ? Ans. 5 per cent.

2 At what rate per cent will 400l amount to 5041 19s 9d 9.2qrs in 4 years ? Abs. 6 per cent.

3 At what rate per cent will 480l amount to 6431 4s 11 1d in 6 years ? Answer 5 per cent.

4 At what rate per cent will 500l amount to 5901 11s 5d 3qrs in 4 years ? Answer 41 per cent. OF ANNUITIES, OR PENSIONS IN ARREARS.

CASE 1. Note. U represents the Annuity, Pension, &c. T, R & A as be. fore.

Q. When U, T, and R, are given to find A, how is it discovered?

t A. Thus; ür

EXAMPLES : What will an annuity of 30% per ann. payable year

P

ly, amount to in 4 years, at 5 per cent? Ans. 1291 65 Od 3.6qrs.

2 Suppose a Pension of 501 per ann. payable yearly, be granted to a superannuated Officer ; what is the amount for 5 years forbearance at 4 per cent ? Ans. 2701 16s 3d 3.4 + qrs.

3 If the yearly rent of a house which is 40l be forborn 7 years at 6 per cent. what is the amount ? Ans. 3351 158 od 3.3+qrs.

4 If a salary of 35l per annum to be paid yearly, be omitted for 6 years at 51 per cent. what is the amount? An. 2411 18 7d 2.5qrs.

Q. When R, T, and A, are given to find U, how is it discovered ?

CASE 2.

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1 What annuity, being forborn for 4 years, will amount to 1291 68 1d at 5 per cent'Ans. 301 per ann.

2 If a pension being forborn for 5 years, at 4 per cent. per annum amounts to 270l 16s 4d I demand how much it is per ann? Ans. 50l per ann.

3 If the yearly rent of a house, being forborn' for 7 years,

at per cent amounts to 3351 158 Od 3.4qrs. I demand what the rent is ? Ans. 401 per ann.

4 If the payment of a salary be omitted 6 years ; I demand how much the salary is, when the amount is 2411 15 3d 2.6 qrs at 54 per cent ? Ans. 351 per ann.

CASE 3, Q. When U, A, and R, are given to find T, how is it discovered?

which being continually diviatru-a ded by r, till nothing remains, A. Thus ;

the Number of those divisions will be=t.

t

U

EXAMPLES.

1 In what time will 301 per annum amount to 1291 6s id allowing 5 per cent for the forbearance of payment ? Ans. 4 years.

2 In what time will a pension of 501 per annum amount to 270! 6s 4d at 4 per centi Ans. 5 years.

3 In what time will the yearly rent of a house, being

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