8. At 6%, what is the interest of $850 for 8 mo.? 9. What is the amount of $50.50 for 1 yr. 3 mo., at 6 %? 10. What is the amount of $300, at 6%, for 10 days? 11. I owe a merchant $540 and agree to pay him the debt in 30 days, with interest at 6%; how much shall I have to pay him? 12. I buy a property for which I agree to pay $1000 cash, $1000 in 3 months, and $1000 in 6 months, with 6% interest; what will the property have cost me when the final payment is made ? 13. I borrow $500, January 13, 1875, and pay it July 5, 1875, with 6% interest; what does the use of the money cost me? 14. What is the amount of $420.80 from July 9, 1876, to December 25, 1876, at 6% ? 15. What is the interest, at 6%, on $120, borrowed on Christmas, and paid on New Year's Day, counting both days? 16. If I borrow $320, May 1, 1877, and pay it with 6% interest December 31, 1877, how much do I pay? 17. What is the interest of $800 for 1 yr. 2 mo., at 8%? 1 yr. 2 mo. = 420 days. ANALYSIS.—We find the $800 X 420 interest at 6% to be $56.00; - = $56.00. and if the interest at 6% = $56.00, the interest at 8%= of $56.00 = $74.66. of $56.00= $74.66. 18. What is the interest of $326 for 1 yr. 3 mo. 10 da., at 41%? At 5%? At 8%? At 10%? 19. What is the interest of $96.50 for 90 days, at 3% ? At 7%? At 124%? At 15%? 20. A note dated March 30, 1870, was paid July 6, 1870, with interest at 7%; what was the amount? CASE II. The interest, or amount, and the rate and time, being given, to find the principal. WRITTEN EXERCISES. 1. I wish to lend such a sum of money at 6%, for 3 years, as will yield me $54 interest. ANALYSIS.—We find Interest of $1 for 3 yr.=$.18. that the interest of $1 $54 • .18= $300. for 3 years at 6% is $.18. Now, if $1 of. principal produces $.18 interest, to produce $54 interest will take as many dollars of principal as .18 is contained times in 54= 300, the number of dollars required. RULE. Divide the given interest by the interest of one dollar for the given time and rate; or, divide the given amount by the amount of one dollar for the given time and rate. 2. At 5%, what principal will produce $4.621 in 1 yr. 6 mo. 15 da. ? 3. At 6%, what principal will produce $300 interest in 16 yr. 8 mo.? 4. A man wishes to provide an annual income of $1000 for his wife; what sum must he put at interest, at 6%, to produce that sum? 5. What principal will amount to $490.50 in 1 yr. 6 mo., at 6%? 6. I desire to put a certain sum at interest, at 6%, for 18 months, so that at the end of that time I shall have $228; what sum must I invest? 7. What principal, at 8%, will amount to $180 in 1 year? 8. If I receive $28.50 as the interest due on money lent at 11% a month for 4 months, what sum did I lend? 9. A church wishes to secure to the pastor an income of $100 per month; what sum invested at 6% will yield that amount? 10. I have a mortgage of $900 on my property, due in 18 months; how much must I invest now, at 5%, to amount in that time to the required sum? CASE III. The principal, interest, and time, being given, to find the rate. WRITTEN EXERCISES. 1. At what rate will $400 yield $30.664 in 1 yr. 3 mo. 10 da. ? The interest of $400 for 1 yr. 3 mo. 10 da., at 1%= $5.111. 30.664 = 5.111 = 6. ANALYSIS.—If $400, at 1%, for 1 yr. 3 mo. 10 da., yields $5.11}, to yield $30.66 for the same time will take as many % as 5.114 is contained times in 30.66%, which=6. The rate, therefore, is 6%. RULE. Divide the given interest by the interest of the given principal for the given time at one per cent. 2. At what rate will $180 yield $27 interest in 3 years ? 3. At what rate will $600 amount to $684 in 2 yr. 4 mo.? 4. I lent $500 for 2 yr. 4 mo., and received at the end of that time $552.50 in full; what was the rate %? 5. At what rate will any sum double itself in 16 yr. 8 mo.? 6. My semi-annual interest on ten 500-dollar government bonds is $150; what is the rate per cent.? 7. My annual income on $800 invested in Kansas, at the legal rate, is $80, while the same amount invested in New Jersey at the legal rate yields only $56; what is the difference in the rates ? 8. At what rate will I have to invest $15000 so that it may yield me $300 quarterly? CASE IV. The principal, rate, and interest, being given, to find the time. 1. How long will it take $500 to gain $45, at 6 %? The interest of $500 for 1 year at 6%= $30. $45 - $30 = 11. 11 yr. =1 yr. 6 mo. ANALYSIS.—If $500 gains $30 in 1 year, at 6%, to gain $45 at the same rate will take as many years as $30 is contained times in $45, which=11. 11 years=1 yr. 6 mo. RULE. Divide the given interest by the interest of the given principal at the given rate for one year. 2. I lent a friend $1300, at 6%; at settlement he owed me $1339; how long did he have the money? 3. In what time will $1250 gain $500, at 7%? 4. In what time will $1920 amount to $2178, at 6%? 5. In what time will $500 double itself, at 6%? At 5%? 6. In what time will $1800 amount to $1964, at 4%? 7. A young man, on coming of age, received $1798.50 as the amount of a legacy of $1650, at 6%; how old was he when the money was invested? COMPOUND INTEREST. Compound Interest is interest on both principal and interest, if the latter is not paid when due. Note.-Interest may be compounded at whatever time it is made payable, as, annually, semi-annually, etc. It is not considered usury, but it cannot be collected by law. 1. What is the interest of $500 for 3 years, compounded annually, at 6%? Principal ...... $500 Compound Interest . . . $95.50 ANALYSIS.—In this example the interest being compounded annually, we find the interest for one year, and add it to the principal, forming a new principal, on which we calculate the next year's interest, and so on. The first principal subtracted from the final amount gives the compound interest. RULE. Find the amount of the given principal for the first period for which it is to be compounded; proceed with this amount as a new principal for the second period, and so on; the difference between the last amount and the given principal will be the compound interest. Note. When there is a partial period, the interest for that time is to be computed on the last amount and added to it. |