What is the interest of $ 162,14 for 2 years and 4 months at 7 per cent ? Ans. $ 26,482. What is the interest of $ 64,18 for 1 year and 10 months, at 4 per cent ? Ans. $ 4,706. It frequently happens that the debtor wishes to make partial payments of his Bonds, Notes, &c. Interest on obligations of this description, is cast in the following manner, as established by the courts of law in Massachusetts : “Cast up the interest to the time of the first payment, and if the payment exceed the interest, deduct the excess from the principal, and cast the interest upon the remainder to the time of the second payment. If the payment be less than the interest, place it by itself, and cast on the interest to the time of the next payment, and so on until the payments exceed the interest ; then deduct the excess from the principal, and proceed as before." A. held a note against B. of $246, 24 dated October 12, 1822. March 12, 1823, paid $ 68 ; what was due, September 24, 1823 ? The sum may be prepared by first finding the time from the date of the note to the first payment, and from the first payment to the final payment, and placing them as follows. $68,00 | Mon. Days. March 12, 1823, Ans. $190,296. In this example you first cast the interest on the whole sum to the time of the first payment. Now if the first payment had been just the amount of interest then due, the principal would have remained the same, and the interest continued as though nothing had been paid. But in this case there was much more paid than the amount of the interest; and hence the reason of deducting the excess from the principal. After having deducted the excess from the principal, you have the amount then due, and must cast the interest on it to the time of final payment. Mon Days A. holds a note against B. of $866, dated June 20, 1820, on which were the following payments. April 20, 1821, $40; Aug. 20, 1821, $462 ; what was due Jan. 14, 1822 ? April 20, 1821, $ 40 10 00 August 20, 1821, 462 4 00 To Jan. 14, 1822. 4 24 Ans. $ 434,81. In this example you first cast the interest to the time of the first payment, and find it exceeds the payment, or the payment is not enough to pay the interest ; therefore cast on to the time of the next payment, and add this interest to the interest from the date to the first payment; add the two payments together and subtract the interest from their sum ; then deduct the excess from the principal, and proceed as in the former exampie. A., holds a bond against B. for $1166,666, dated May 1, 1804, upon which the following payments have been made. 1. December 25, 1804, $166,666 7 24 2. July 10, 1805, 16,666 6 15 3. September 1, 1806, 50,000 13 21 4. June 14, 1807, 333,333 9 13 5. April 15, 1808, 620,000 10 1 What will be due upon it Aug. 3, 1809 ? 15 18 It is convenient in casting interest on bonds, notes, &c. of the above description, to arrange the work as in the following table. | Principal. | Time. | Interest. | Payments | Excess. 1 $1166,666 7 24 $45,499 $166,666 $121,167 121,167 Mon. Days. 1. Mon. Days. | 5 579,847 800,406 10 1 40,153 620,000 220,559 I 2 COMPOUND INTEREST Is calculated by adding the interest to the principal at the end of each year, and making the amount the principal for the succeeding year ; then the given principal subtracted from the last amount, the remainder will be the compound interest. What is the compound interest of $ 216,42 for 2 years and 6 months ? 216,42 6 12,9852 interest for 1 year. 216,42 229,40 principal for 20 year. 6 13,7640 interest for 2d year. 3 7,2948 interest for last 6 months. 34,03 compound interest for 2 years and 6 mo. The-compound interest at 6 per cent of any sum in Federal Money may be found by multiplying the sum by the following numbers. For 2 years multiply the given sum by 112,36 For 7 years, by 150,3630 3 years, 119,1016 8 years, 159,3848 4 years, 126,2476 9 years, 168,9478 5 years, 133,8225 10 years, 179,0847 6 years, 141,8519 11 years, 189,8298 Point the product as in simple interest ; when it will show the amount of principal and interest for the given number of years. Subtract the principal from the amount, and the remainder will be the compound interest. When there are months and days, first find the compound interest for the given years ; then, for the months and days cast the simple interest on the amount for the years, which, added to the amount, will give the answer. Any sum'at compound interest will double in 11 years, 10 months, and 22 days. What is the compound interest on $246, for 2 years ? *Ans. $ 30,40. What is the compound interest on $236, for 4 years, 7 months, and 6 days? Ans. 72,669. Questions. swer ? What is interest ? How does it appear that it is right to allow interest for money borrowed? What is the money lent called ? How many kinds of interest are there, and what are they called What is simple interest ? Why do you place a cipher at the right of half the even number of months, when the days do not amount to 6 ? Why do you point off two more places for decimals, in the product than there are decimals in both the factors ? How do you find the interest for any other rate than 6 per cent ? How do you cast the interest on bonds, notes, &c. where partial payments have been made ? Why do you deduct the excess from the principal ? When the payment is less than the interest, wby do you cast on to the time of the next payment? How do you cast compound interest? Examples for Practice. 1. What is the interest of $264,16 for 2 years and 6. months ? Ans $39,624. 2. What is the interest of $64,18 for 3 years, 5 months, and 7 days ? Ans. $13,231. 3 What is the interest of $5,811 for 1 year and 11 months ? Ans. $0,668. 4. What is the interest of $86 for 9 months ? Ans. $3,87. 5. What is the interest of $78,36 for 5 years, 10 months, and 3 days ? Ans. $27,465. 6. What is the interest of $246,25 for 1 year, 5 months, and 5 days, at 3 per cent ? Ans. $10,568. 7. What is the interest of $812,30 for 2 years, 8 months, and 4 days ? Ans. $130,509. 8. What is the interest of $5,19 for 7 months ?. Ans. $0,181. 9. What is the interest of $1,07 for 3 years, 6 months, and 15 days ? Ans. $0,227. 10. What is the interest of $273,51 at 7 per cent, for 1 year, and 10 days ? Ans. $19,677. 11. What is the interest of $200,06 for 1 year and 4 days? Ans. $13,337 12. What is the interest of $0,001 for 16 years and 8 months ? Ans. $0,001. 13. What is the interest of $0,0005 for 33 years, and 4 months ? Ans. $0,001. 14. What is the interest of $2586974 for 30 years 2 Ans. $4659553 and 20 cts. 15. Supposing a note of $867,33 dated Jan. 6. 1794, upon which the following payments should be made, viz. 1. April 16, 1797, $136,44 518,68 What would be due July 11, 1801 ? Ans. $215,103. |