EXAMPLES. 1. At 18%, the premium for insuring my store was $89.10; what was the amount of the insurance? Ans. $6480. 2. The premium for insuring a tannery for of its value, at 13%, was $145.60; what was the value of the tannery? Ans. $11648. 3. A store and its goods are worth $6370. What sum must be insured, at 2%, to cover both property and premium? Ans. 4. The premium for insuring $9870 was $690.90; what was the rate? Ans. 7%. 5. A merchant whose stock of goods was valued at $30000, insured it for of its value, at %. In a fire he saved $5000 of the goods. What was his loss? What was the loss of the insurance companies? Ans. 6. A man paid $180 for insuring his saw mill for of its value at 3%; what was the value of the mill? Ans. 7. A house which has been insured for $3500 for 10 years, at % a year, was destroyed by fire; how much did the money received from the company exceed the cost of premiums? Ans. 8. Took a risk on a house worth $40000, at 2%; reinsured of it for 24%, and of it at 24%; in each case the amount cov. ers premium; how much do I gain? Ans. $99.558. 9. Took a risk at 1%; reinsured of it at 21%; my share of the premium was $43; what was the amount of the risk? Ans. $17200. 10. Took a risk at 24%; reinsured of it at a rate equal to 3% of the whole, by which I lost $37.50. What was the value of the risk? Ans. $5000. CHAPTER XIII. INTEREST. I. SIMPLE INTEREST. 1. Interest is money paid by the borrower to the lender for the use of money. 2. The Principal is the sum of money for which interest is paid. 3. The Rate of interest is the rate per cent. on $1 for a certain time. 4. The Time is the period during which the money is on interest. 5. The Amount is the sum of the principal and interest. 6. Simple Interest is interest on the principal only. 7. Legal Interest is at the rate fixed by law. 8. Usury is interest at a rate greater than that allowed by law. Let P the principal, r the interest on $1 for one year, A amount of P for n years, Pr=simple interest on P for a year, Pur-simple interest on P for n years. P+Pnr=P (1+nr)=amount of P for n years. :. A=P+Pnr=P(1+mr). ... (I.); When any three of the quantities A, P, n, r are given, the fourth may be found. Principal, CASE I. Given Rate, and to find the interest. Formula, I-Prn. Time, I. Find the interest of $300 for two years at 6%. (1. 100% II.2. 1% of $300-$3, and 3. 6%-6 times $3-$18-interest for one year. ... $36 interest on $300 at 6% for 2 years. III. CASE II. Principal, A-P Given Rate, and to find the time. Formula, n= Interest, I. In what time, at 5%, will $60 amount to $72? n= A-P $72-$60 Pr =4 years. $60X.05 By 100% method. (1. $72-amount. 2. $60 principal. 3. $72-$60-$12-interest for a certain time. II.4. 100% $60, 5. 1% of $60-$3, and 6. 5%-5 times $3-$3=interest for one year. III... $60 at 5% will amount to $72 in 4 years. Pr CASE III. Principal, A-P Given Time, and to find the rate. Formula, r= Pn Interest, I. I borrowed $600 for two years and paid $48 interest; what I. The interest for 3 years, at 9%, is $21.60; what is the principal? Time, Given Rate, and to find the principal. Formula, P= A 1+nr I. What principal will amount to $936 in 5 years, at 6%? 4. 100% +30%=130% 5. $936 amount. 6... 130% $936, interest for 5 years. 7. 1%=13% of $936=$7.20, and 8. 100% 100 times $7.20 $720=principal. III. .. $720 the principal that will amount to $936 in 5 years at 6%. I. In what time will any sum quadruple itself at 8%? 1. 100% principal. Then 2. 400% the amount. II.3. .. 400%-100%-300%=interest. 4. 8% interest for 1 year. 5. 300% interest for 300-8, or 37 years. III. ... Any principal will quadruple itself in 37 years at 8%. II. TRUE DISCOUNT. 1. Discount on a debt payable by agreement at some future time, is a deduction made for "cash," or present payment; and arises from the consideration of the present worth of the debt. 2. Present Worth is that sum of money which, put on interest for the given time and rate, will amount to the debt at its maturity. 3. True Discount is the difference between the present worth and the whole debt. Since P will amount to A in n years, P may be considered equivalent to A due at the end of ʼn years. .. P may be regarded as the present worth of a given future sum A. A I. Find the present worth of $590, due in 3 years, the rate of interest being 6%. By formula, II.< 1. 100% 2. 6% interest on present worth for 1 year. 3. 18% 3×6%=interest for 3 years. 5. $590-debt. 6... 118% 7. 1% $590, amount, or debt. of $590-$5, and 8. 100% 100 times $5-$500-present worth. III... $500-present worth of $590 due in 3 years at 6%. |