That the interest of the money paid in before the time, be deducted from the interest of the whole sum due at the time appointed by the instrument for making the payment. EXAMPLES. A received of B his note for $100, dated January 1st, 1820, payable in one year, with six per cent: interest. And 1820, July 1st, A received of B fifty dollars, which A credited on said note-what was the balance due from B to A, on January 1st, 1821 ? In this case $54.50 is the equitable balance. 1.50 54.50 $106.00 If the above note had been on demand, or due at the time the payment was made, (July 1st, 1820,) the balance on the 1st of January, 1821, would have been $54.59: thus, Interest of $100 for 6 months, to July 1, 1820, Balance of the note after the first payment, Making a difference of 9 cents. A note, dated January 1, 1795, was given for $240, payable in one year after date, at six per cent., and there were payments endorsed upon it as follows, viz. first payment, $100, June 1st, 1795; second payment, $80, October 1st, 1795-I demand how much remains due on said note, the first day of January, 1796? Ans. $69.70 balance. This rule is perfectly correct when partial payments are endorsed before the note is due; in all other cases, the resort must be to the rule of court for the district where the business is transacted. EXAMPLES. A bond or note, dated January 1, 1795, was given for $240 on demand, bearing interest at six per cent., on which were endorsed the following payments-viz. first payment, $100, June 1, 1795; second, $80, October 1, 1795:-I demand how much remained due on said note, the first day of January, 1796? Ans. $69.95,38. See the difference in the two last examples. A general rule of Courts for computing interest. Compute the interest to the time of the first payment; if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total: if there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and in like manner from one payment to another, till all the payments are absorbed, provided the time between one payment and another be one year or more. But if any payment be made before. one year's interest hath accrued, then compute the interest on the principal sum due on the obligation for one year, add it to the principal, and compute the interest on the sum paid from the time it was paid, up to the end of the year; add it to the sum paid, and deduct that sum from the principal and interest added as before. If any payments be made of a less sum than the interest arisen at the time of such payments, no interest is to be computed, but only on the principal sum for any period. SIMPLE INTEREST. CASE 2. The amount, time, and rate per cent. being given, to find the principal. RULE. As the amount of $100, at the rate and time given, Is to the amount, (or sum given,) So is $100 principal, To the principal required, (or present worth.) EXAMPLES. 1. What principal, at interest for four years at six per cent., will amount to 496 dollars? 2. What sum, at interest for four years at five per cent. per annum, will amount to $571.20 ? Ans. $476. 3. What sum, at interest for 8 years at six per cent., will amount to $925? Ans. $625. 4. What principal, at interest for 2.5 years at six per cent., will amount to $718.75? Ans. $625. 5. What principal, being put to interest for 16 years at seven per cent. per annum, will amount to $65.72? CASE 3. Ans. $31. The amount, time, and principal being given, to find the rate per cent or ratio. RULE. Subtract the principal from the amount, and the remain der is the interest: then say, As the product of the time and principal Is to $100, So is the interest for the whole time To the rate per cent. Or, annex two ciphers to the interest, and divide the sum by the product of the principal and time, and the quotient will be the per centage. N. B. Divide the per centage by 100 for the ratio. EXAMPLES. 1. At what rate per cent. will $500 amount to $650 in five years? 4. At what rate per cent. will $225 amount to $285.75 in 4 years ? Ans. 6. 5. At what rate of interest per annum, will $31 amount to $65.72 in 16 years? Ans. 7 per cent. CASE 4. The rate per cent., principal, and amount given, to find the time. RULE. As the interest of the principal for one year at the given rate, Is to the whole interest, So is one year, To the time required. EXAMPLES. 1. In what time will $500 amount to $725, at five per Ans. 9 years. $500×5-$25.00, int. 1 year 2. In what time will $837 amount to $1029.51, at 5.75 per cent. per annum? Ans. 4 years. 3. In what time will $1600 amount to $2752, at six per cent. per annum? Ans. 12 years. 4. A testator left his son, after providing for his education, &c. $1500, to receive the amount, at six per cent. per annum when he should arrive at the age of 21 years, which his guardian then paid, amounting to $2332.50-how old was the boy at his father's decease? 8.25 Ans. 11 years 9 months, or 11.75y. DISCOUNT. DISCOUNT is an allowance made for payment of money before it becomes due. The present worth of a debt, payable at a future time, is such a sum as being put to interest at a given rate per cent. per annum, during the time by which the payment is anticipated, would amount to the given debt. (It is to find the principal, when the amount, time, and rate per cent. per annum are given.) See Case 2 in Simple Interest. RULE. Assume any principal at pleasure, and find the amount for the time and rate per cent. Then, as the amount found, Is to the amount or debt given, So is the principal assumed, To the required principal, or present worth. The present worth subtracted from the given sum will give the discount. Or, If the interest of the assumed principal be made the third term in the above statement, the fourth term will be the discount. EXAMPLES. 1. What is the present worth and discount of $535, payable in 15 months, allowing discount at six per cent. per annum? Then, interest on $100 for 15 months=$7.50 Assume $100 add 100 $107.50 amount 107.5)53500.0(497.67+present worth. C. Then, $535-497.67+$37.33 discount. Or, As 107.5 : 7.5 :: 535 : $37.33 (nearly) discount. NOTE. This method of computing discount is the equitable one; the interest being really estimated at the proposed per cent. per annum. The mode generally adopted at the banks is, to compute |