(2) What is the interest of 500l. from May the 12th, 1784, to November the 24th, 1789, at 34 per cent. per ann.?

Case 2. When the interest required is for days only.

RULE.

Multiply the interest of 1. for one day, at the given rate, by the principal and number of days; it will give the an

swer.

The interest of 17. for one day is thus found:

(3) What is the interest of 3707. 10s. for 220 days, at 4 per cent. per annum ?

(4) What is the interest of 6007. from the 1st of July, 1789, to the 24th of February following, at 6 per cent. ?

Case 3. When the principal, time, and rate per cent. are given, to find the amount.

RULE.

Find the interest by Theorem 1, which, added to the principal, will give the amount.

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Thus, THEOREM 2. p t r.+p=A.

EXAMPLES.

(5) What will 2347. 10s. amount to in 7 years, at 3 percent. per annum?

(6) What will 6721. 5s. amount to in 5 years, at 44 pér cent. per annum ?

(7) What will 500l. amount to in 6 years 120 days, at 43 per cent. per annum?

Case 4. When the rate, time, and interest are given, to find the principal.

RULE.

Divide the interest by the product of rate and time, the quote is the principal.

(8) I demand what principal, being put to interest for 3 years, will gain 697. 13s. 6d. at 5 per cent. per ann. (9) I demand what principal, being put to interest for 5 years, will gain 647. 78. at 43 per cent. per ann.

(10) I demand what principal, being put to interest for 4 years, at 4 per cent, will gain 67%. 15s. 9 d.

Case 5. When the amount, rate, and time are given to find the principal.

RULE.

Add 1 to the product of the rate and time, and by that sum divide the amount: the quote is the principal.

(11) What principal, being put to interest, will amount to 3541. 4s. Ožd. in 7 years, at 3 per cent. per annum ? (12) What principal, being put to interest, will amount to 500l. 9s. 3 d. in 6 years 5 months, at 5 per cent. per

annum ?

(13) What principal, being put to interest for 7 years 220' days,at 4 per cent. per annum, will amount to 1007.?

Case 6. When the principal, interest, and rate are given, to find the time.

RULE.

Divide the interest by the product of the principal and rate : the quote is the time.

(14) In what time will 4647. 10s. gain 691. 138. 6d. at 5 per cent. per annum?

(15) In what time will 2601. gain 647.7s. at 4 per cent. per annum ?

(16) In what time will 500l. gain 130l. 9s. 7d. at 64 per cent. per annum?

Case 7. When the principal, interest, and rate are given, to find the time.

RULE.

Divide the amount, less the principal, by the product of the principal and rate: the quote is the time.

(17) In what time will 2847. 10s. amount to 3541. 48. Ožd. at 34 per cent. per annum?

(18) In what time will 672l. 5s. amount to 8471. 17s. 6d. at 44 per cent. per annum ?

(19) In what time will 3787. 18s. amount to 500l. 9s. 3žd. at 5 per cent. per annum.?

Case 8. When the principal, interest, and time are given, to find the rate per cent.

RULE.

Divide the interest by the product of the principal and time the quote is the rate.

(20) At what rate per cent. will 4647. 10s. gain 69l. 13s. 6d. in 3 years?

(21) At what rate per cent. will 2601. gain 641. 7s. in 51⁄2 years?

(22) At what rate per cent. will 560l. 12s. 3 d. gain 2351. 9s. 4d. in 7 years?

Case 9. When the principal, amount, and time, are given, to find the rate.

RULE.

Take the difference between the amount and principal, and divide it by the product of the principal and time: the quote

is the rate.

23) At what rate per cent. will 2847. 10s. amount to 354/. 4s. Od. in 7 years?

(24) At what rate per cent. will 3781. 18s. amount to 500l. 9s. 34d. in 6 years?

(25) At what rate per cent. will 6721. 5s. amount to 8471. 17s. 6d. in 5 years?

LXII. Of ANNUITIES, PENSIONS, &c. in ARREARS, at SIMPLE INTEREST.

AN annuity is a yearly income arising from money &c and is either paid for a term of years, or upon a life

Annuities or pensions are said to be in arrears when they are payable or due either yearly, half-yearly, or quarterly, and are unpaid for any number of payments.

Here U represents the annuity, pension, or yearly rent, A, T, R, as before.

Case 10. When U, R, and T are given, to find A.

When the annuity, &c. is to be paid half-yearly, or quarterly, then for half-yearly payments take half the ratio, half the annuity, &c. and twice the number of years; and for quarterly payments take a fourth part of the ratio, a fourth part of the annuity, and four times the number of years; which work with as per theorem.

EXAMPLES.

(26) If 250l. yearly rent, pension, &c. be forborne or unpaid 6 years, what will it amount to in that time, at 3 per cent. for each payment, as it becomes due?

(27) If a salary of 2501. payable every half-year remain unpaid for 6 years, what would it amount to in that time, at 3 per cent. per annum?

(28) If a salary of 250l. payable every quarter, were left unpaid for 6 years, what would it amount to in that time, at 3 per cent. per annum ?

It may be observed, by comparing the answers of the three last Examples, that the half-yearly payment is more advantageous than the yearly one, and also the quarterly more than the half-yearly.

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

C When the payments are half-yearly, take 4a; if quarterly, sa; and proceed with the ratio and time as before.

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