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Thus may the Examples of Case 3rd be done.

Annuities and Pensions in Arrear.

An Annuity or Pension supposed payable upon the day it becomes due; but if it be withheld or forborn, i. e. remain unpaid beyond the day, it is said to be in Arrears.

Now if an annuity payable yearly be in arrear, and it is required to know what the same will amount to, simple interest being computed for every particular yearly payment from the time it became due until the time it is paid, how to calculate this we shall shew in the following

Examples.

1. If an annuity of 70l. be forborn 5 years, what will be due for principal and interest at the end of said term, simple interest being computed at 5 cent. annum?

Rule.

1. Find the interest of the given annuity for 1 year. 2. And then for 2, 3, &c. years upon the given time less 1. 3. Multiply the annuity by the number of years given. 4. Add the several interests and the said product

into one sum.

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2. If the payment of a pension be omitted for 7 years, what will it amount to in that time at 6

cent. supposing it 561. annum ? Answ. 4621. 118. 2zd.

3. A house being let upon a lease of 7 years, at 50%. annum, and the rent being in arrear for the whole term, I demand the sum due at the end of the term, simple interest being allowed at 4 cent. anuum ?

Answ. 3921,

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5. If any annuity or yearly rent of 1347. 10s. 6d. be all forborn till the end of 4 years, what will it then amount to; simple interest being allowed at the rate of 6 cent. annum? Answ. 5861. 10s. 6d.

But if simple interest were allowed upon half-yearly or quarterly payments, it would be still more in favour of the receiver.

Find the interest of the last payment but one, and then of the other as before, viz.

6. If 70l. annuity, payable every half year, were unpaid 5 years, what will it amount to in that time at 5 cent.?

Last payment but one, half-a-year's annuity 351.

Yr.

1. 8. d.

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R

CHAP. VI.

REBATE OR DISCOUNT.

EBATE or Discount is an allowance made upon any sum of Money being paid before it becomes due; or upon advancing ready Money for Bills, Notes, &c. which are payable at a future day. And this allowance is sometimes computed at so much Pound Sterling, and sometimes at so much Cent, per Annum, Simple Interest.

1. Discount computed per Pound Sterling.

Discount at so much per pound sterl. may be computed by aliquot parts, viz. dividing the given sum to be discounted by the denominator of that part which the discount of 11. is of 17. The quotient is the discount, which being subtracted from the given sum, the remainder is the sum to be advanced in ready money.

Examples.

1. Bought goods of A B, amounting to 1277. 13s. 4d. and for prompt payment am allowed 6d. in the pound; I want to know how much I must pay him?

Decimally.
127 6

1. S. d.

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0.25 6d.

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2. Changed Nathan Needy, Richard Drawer's bill on Peter Paywell of Cork, at 31 days sight, for 1541. at 2d. per 7 discount, how much ready money must I pay for said bill? Answ. 1521. 14s. 4d.

3. How much ready money must I advance for 5721. 17s. 8d. discount being allowed at 4d. per l. ?

Answ. 5631. 6s, 84d.

4. Bought 6 pipes of wine, each 121 gallons, at 4s. 9d. per gallon by auction, and for prompt payment am allowed Is. per pound discount, what must İ pay for said wine?

Answ. 165t. 16s. 09d.

2. Discount computed at a given Rate per Cent. per Annum. If 106 100. gen sum; its present worth or pay ment, it shall be 190: (106--100)6: any sum to be rebat ed to the same sum less its present worth, i. e. to the rebate. Note.

Note. The rebate subtracted from the sum discounted leaves the present worth, et contra.

Examples.

5. A merchant buys certain merchandizes to the value of 6481. payable in 12 months; how much ready money must he pay rebate at 8

cent.

annum?

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Find the amount of the present payment at the time and rate given, and that will be equal to the given sum to be rebated.

100

-108

-600

to oome,

600 648160

6. If a debt of 1001. 6s. be payable at the end of a year how much ready money will discharge the debt at the rate of 6 cent. ann? Answ. 941. 12s. 533d. 7. What is the rebate of 451. 15s. 6d. for 12 months, at 6 cent. annum? Answ. 21. 118. 943d.

8. I demand how much ready money I must pay for 4321. 14s. for 12 months, rebate at 7 cent. annum? Answ. 4011. 7s. 10,3d.

When any other time beside a year is given, find the interest of 100 for that time at the given rate, which must be added to 100 for the first number, as in the following

Examples.

9. What is the rebate of 7951. 11s. 2d. for 11 months, cent, annum?

at 6

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10. What ready money must I pay for 1611. 10s. dug in 19 months, discount being allowed at 5 annum? Answ. 1491. 13s. 03d.

cent.

11. Bought goods amounting to 7951. 11s. 2d. at 4 months credit, how much ready money must I pay discount at 31 cent. annum ? Answ. 7861. 7s. 8d.

12. What is the present worth of 40001. payable in 9 months at 43 cent. ann.? Answ. 38621. 8s. Ožd.

13. Tell me the rebate of 1121. 12s. for 20 months, at 7 cent. annum? Answ. 111. 15s. 327d. 14. Some merchandizes being bought for 51501. with

4 months

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