3. What is the amount of $500 for 9 years, at 6 per cent. per annum, the interest to be paid semi-annually?

As the time, t, is to be calculated in half-years, and as r is considered the interest of $1 for one year, therefore 2t will

represent the time, and the interest of $1 for half a year.

4. What principal, at compound interest, will amount to $4000 in 10 years, at 6 per cent.?

This question must be performed by the second formula.

5. At what rate per cent. must $2233.57 be, at compound interest, to amount to $4000 in 10 years?

This question should be performed by the third formula.

6. In what time will $2233.57, at compound interest, at 6 per cent., amount to $4000?

This question is solved by the fourth formula.

The value of this fraction can be ascertained by logarithms.

7. What will $16 amount to in 30 years, at 5 per cent. compound interest?

Ans. $69.15.

8. What will $2000, at compound interest, amount to in 11 years, at 8 per cent.?

9. What will $27.18 amount to in 8 cent. compound interest?

Ans. $4663.31.

years,

3 months, at 4 per

Ans. $37.56.

10. What is the compound interest of $1728 for 8 years, 6 months, at 6 per cent. per annum, the interest to be paid every 3 months? Ans. $1338.74.

11. What is the amount of $18.29 for 8 years, 8 months, 12 days, at 4 per cent.? Ans. $25.73.

12. What sum, at compound interest, will amount to $800 in 7 years, at 5 per cent. compound interest?

Ans. $568.54.

13. What sum will amount to $500 in 9 years, at 6 per annum, the interest to be paid every 3 months?

per cent.

Ans. $292.54.5.

14. At what rate per cent. will $800, at compound interest, amount to $1609.76 in 12 years? Ans. 6 per cent.

15. In how many years will $3726 amount to $5007.43, at 3 per cent. compound interest? Ans. 10 years.

16. How many years will it require for any sum to double itself, at 6 per cent. compound interest?

Therefore 301030-11.89 years. Ans.

17. How many years will it require any sum to triple itself, at 5 per cent. compound interest? Ans. 22 years, 188 days.

18. In 1840, the number of inhabitants in the United States was 17,068,666; in 1850, the number was 23,267,498. What was the gain per cent. per annum ? Ans. .03146 per cent.

19. At the same rate as in the last will there be 100,000,000 inhabitants?

question, in what year Ans. May 3d, 1897.

- This answer is on the presumption that the census is taken the

NOTE. first day of May.

20. Required the compound interest upon $155, for 9 years, at 31 per cent. Ans. 56.24+.

21. Required the amount of $820 for 2 years, at 41 per cent. per annum, the interest being paid half-yearly.

Ans. $916.49+.

22. What sum at compound interest, for 24 years, at 41 per cent., the interest payable every six months, will amount to $458.25? Ans. $410.02.

23. At what rate per cent. will $2000, at compound interest, amount to $4663.34 in 11 years?

Ans. 8 per

cent.

DISCOUNT AND PRESENT VALUE AT COMPOUND INTEREST.

313, Let

p = the present value.

s the sum due.

t = the time.

d the discount.

Then, by principles before explained, we have the following

1. What is the present worth of $600, due 3 years hence, at 6 per cent. compound interest?

Ans. $503.77.

2. John Smith, Jr., owes me $312.50, which is due 2 years hence, at 4 per cent. compound interest. discharge the debt?

What sum will now

Ans. $286.16.

3. What is the present value of $1000, due 4 years hence, at

5 per cent. compound interest?

Ans. $822.70.

4. What is the discount on $3700, due 10 years hence, at 5 per cent. compound interest?

6

Ans. $1428.51.

5. What is the present worth of $3456, due 5 years hence, at per cent. compound interest? Ans. $2523.74.

6

6. What is the discount on $1000, due four years hence, at per cent. compound interest? Ans. $207.91.

7. Rented a house for 5 years, at $400 a year, the rent to be paid quarterly. What is the present worth of this rent, at 8 per cent. compound interest? Ans. $1653.47.

8. Loaned a friend $100 for one year, at 2 per cent. per month, compound interest; that is, the interest is to be added to the principal each month. What is the amount at the close of the year? Ans. $126.82.

9. Which is the greater present value, $400 due three years hence, at 5 per cent. compound interest, or $500 due 4 years hence, at simple interest? Ans. $500 is better by $71.13.

10. What sum shall I put into the Savings Bank, which pays 5 per cent. compound interest, that shall in 6 years amount to $1000 ? Ans. $746.21.

SECTION XXXI.

DEPOSITS.

ART. 314. A deposit is a sum of money lodged in the hands of some person or corporation, for safe keeping.

1. Deposited annually in a Savings Bank, which pays 6 per cent. compound interest, $144 for 20 years. How much money shall I have in the bank at the end of the 20th year?

By the rule of compound interest, the sum first deposited will amount to 144(1+.06), or a(1+r)'; for the second year,