EXAMPLES.

8. What is the present worth of an annuity of $100, o continue 10 years, at 6 per cent. ?

9. What sum must be invested to yield an annual income of $500, at 6 per cent., for 12 years?

10. What sum must be invested to yield an annual income of $2500, at 5 per cent., for 30 years?

329. To find the present worth of an annuity that is perpetual, or is to continue forever, —

RULE. Divide the annuity by the interest of $1 for 1 year.

EXAMPLES.

11. What sum must be invested at 6 per cent., to yield an annual income of $500?

12. What sum must be invested at 5 per cent., to yield an annual income of $1200?

For what sum

13. A farm rents for $450 a year. should it be sold, when money is worth 5 per cent.? 14. A store rents for $1200 a year. For what sum should it be sold, when money is worth 6 per cent. ?

330. To find the present worth of an annuity in reversion,

RULE. Find the present worth of the annuity for the time before it commences, and also the present worth of the annuity from the present time till it terminates. The difference between these two present worths will be the present worth required.

EXAMPLES.

15. What is the present worth of an annuity of $400 in reversion, at 5 per cent., commencing in 10 years, and continuing 20 years afterwards?

What is the rule for finding the present worth of a perpetual annuity? What is the rule for finding the present worth of an annuity in reversion?

16. What is the present worth of an annuity of $500 at 5 per cent., to commence in 10 years, and to continue 15 years afterwards?

331. To find an annuity, the present worth being given,

RULE. Divide the present worth by the worth of an annuity of $1 for the time and rate.

EXAMPLES.

17. What annuity, at 5 per cent. will pay a debt of $10,000 in 4 years?

18. What annuity, at 6 per cent., will pay a debt of $15,000 in 12 years?

332. To find an annuity, the amount being given, —

RULE. Divide the amount by the amount of an annuity of $1 for the given time.

EXAMPLES.

19. What sum must be invested annually to amount to $5000 in 10 years, at 6 per cent.?

20. What sum must be invested annually to amount to $10,000 in 12 years, at 5 per cent.?

21. What annual sum must be invested as a sinking fund to pay a debt of $20,000 in 10 years, at 6 per cent.?

22. What annual investment will amount to $8000 in 6 years, at 5 per cent.?

23. What sum must be invested annually to amount to $80,000 in 12 years, at 7 per cent.?

What is the rule for finding an annuity, when the present worth is known? What is the rule for finding an annuity, when the amount is known?

EXCHANGE OF CURRENCIES.

SECTION XXXVI.

333. EXCHANGE OF CURRENCIES is changing the denomination of one currency to that of another of equivalent value.

334. Accounts were kept in pounds, shillings, pence, &c., previous to the adoption of federal money in 1786. It is customary with many merchants at the present time to estimate the value of their goods in the old currency of the state.

335. Different values are assigned to the pound, &c., in the different states, as in the following table:

$1-6 s., or £, in New England, Tennessee, Kentucky, Virginia, Mississippi, Missouri, Illinois, and Indiana.

$1=7 s. 6 d., or £3, in New Jersey, Pennsylvania, Delaware, and Maryland.

$1=8s., or £3, in New York, Ohio, Michigan, and North Carolina.

$1=4s. 8 d., or £3, in South Carolina and Georgia. $1=5s., or £4, in Canada and Nova Scotia.

Louisiana, Florida, Arkansas, and Alabama have no currency but federal money.

336. The old par value of a pound sterling was $4.444; but, by a recent act of Congress, the present par value is $4.844, which is 9 per cent. above the old par value. This is now the government value, and is adopted by all the custom-houses. The coin representing a pound is a sovereign.

OBS. The real value of a pound or sovereign of full weight is sometimes estimated at $4.863.

What is exchange of currencies? How were accounts formerly kept? What is the value of a dollar in the currency of each of the states? What is the currency of Louisiana, &c. ?

337. To reduce federal money to any state currency,

RULE. Multiply the given sum by the value of $1 in the required currency, expressed in the fraction of a pound. The product will be pounds. Decimals must be reduced to shillings, pence, and farthings.

1. Reduce $240 to New England currency.

2. Reduce $560 to New York currency.
3. Reduce $780 to Pennsylvania currency.
4. Reduce $840.60 to Georgia currency.
5. Reduce $1200 to Canada currency.

6. Reduce $1600 to Maryland currency.

338. To reduce any state currency to federal money,

RULE. First reduce the shillings, pence, and farthings to the decimal of a pound. Then divide the pounds and decimals annexed by the value of a dollar in the given currency expressed in the fraction of a pound. The quotient will be dollars, cents, and mills. 7. Reduce £72 New England currency to federal

money.

72x=$240.

EXAMPLES.

8. Reduce £240, 10 s. New York currency to federal money.

9.

Reduce £300, 12s. 6d. Pennsylvania currency to federal money.

What is the rule for reducing federal money to any state currency? What is the rule for reducing any state currency to federal money?

10. Reduce £460, 9s. 10 d. Georgia currency to federal money.

11. Reduce £645, 16 s. Canada currency to federal money.

12. Reduce £1200, 15 s. New England currency to federal money.

339. To reduce federal money to English or sterling money,

RULE. Divide the given sum by the value of £1, ($4.844,) and point off the quotient as in the division of decimals, (ART. 120.) The figures on the left of the decimal point will be pounds, those on the right will be decimals, which must be reduced to shillings, pence, &c., as in ART. 150.

13. Reduce $400 to pounds, shillings, &c.

400

4.844-82.576=£82, 11 s. 6 d. 0.96 qr.

EXAMPLES.

14. Reduce $640 to pounds, shillings, &c. 15. Reduce $848 to pounds, shillings, &c. 16. Reduce $100 to pounds, shillings, &c. 17. Reduce $500 to pounds, shillings, &c. 18. Reduce $1000 to pounds, shillings, &c. 19. Reduce $1500 to pounds, shillings, &c.

340. To reduce English or sterling money to federal money,

RULE. Reduce the shillings, pence, and farthings to the decimal of a pound. Then multiply the legal value of a pound, ($4.844,) by the given number of pounds, and point off the product, as in the multiplication of decimals.

What is the rule for reducing federal money to sterling money? What is the rule for reducing sterling money to federal money.