full period, there is still some time for the note to run, treat the last amount found as a new principal, and find the amount for the remaining time. The final amount is the sum due. The difference between this amount and the first principal is the compound interest. 1. What is the amount due on a note for $700, paid 3 years and 4 months from date, interest compounded annually at 7%? What is the compound interest? SOLUTION $700 First principal. .07 49.00 700.00 749.00 Amount for first period of time. New principal. .07 52.43 749.00 801.43 .07 56.1001 Amount for second period of time. New principal. 801.43 857.53 Amount for last full period of time. New principal. .07 3)60.0271 20.00 Interest for remaining time, 4 months. 857.53 877.53 Amount for remaining time, 4 months. Amount due. 2. What is the amount of $300 for 4 years at 6%, interest compounded annually? What is the compound interest? 3. What is the compound interest of $250 for 3 yr. 6 mo. 18 da. at 6 %, interest compounded annually ? Compound interest tables are used in computing compound interest. The table on page 301 shows the amount of $1 at compound interest for any number of years up to 20, and for any rate per cent up to 7. WRITTEN EXERCISES, USING THE TABLE 203. 1. Find the amount of $500 for 20 years at 7%, compound interest. SOLUTION The amount of $1 for 20 years at 7%, as shown by the table (p. 301), equals $3.869684. Hence, the amount of $500 = 500 x $3.869684 = $1934.84. Ans. 2. Find the amount of $800 at 6% for 12 years, compound interest. 3. What is the compound interest at 7% on $2000 for 15 years? 4. Find the amount of $1200 for 9 years at 4%, compounded semiannually. NOTE. When interest is compounded semiannually, one half the given rate and twice the number of periods for which interest is compounded are used. Thus, in problem 4, find the interest at 2 % for 18 years. 5. What is the amount and the compound interest of $400 for 2 yr. 3 mo. at 6%, interest compounded semiannually? NOTE. Compute the interest for 4 yr. at 3%, and then for the remaining time at 6%. 6. Find the compound interest on $5000 for 10 years at 7%, compounded semiannually. 7. What is the difference between the compound and simple interest on $6000 for 6 years at 41%? 8. Formulate and solve a problem in compound interest. YEARS COMPOUND INTEREST TABLE Amount of $1, at various rates, compound interest, 1 to 20 years 1 PER CENT 1 PER CENT 12 PER CENT 2 PER CENT 22 PER CENT 3 PER CENT 7 1.020100 1.025156 1.030225 1.040400 1.030000 1.050625 1.060900 1.045678 1.061208 1.076891 1.092727 1.082432 1.103813 1.125509 1.104081 1.131408 1.159274 1.093685 1.118292 1.159693 1.194052 1.090850 1.109845 1.148686 1.188686 1.229874 1.104486 1.126493 1.171659 1.218403 1.266770 1.143390 1.195093 1.248863 1.126162 1.304773 PRESENT WORTH AND TRUE DISCOUNT 204. The present worth of a debt payable at a future time, without interest, is such a sum as, placed on interest for the time at a certain rate, will amount to the debt. Thus, the amount of $1 for 3 yr., at 6%, is $1.18. Therefore, the present worth of $1.18 due in 3 yr., without interest, is $1. The true discount is the difference between the amount of the debt and the present worth. NOTE. The true discount is the interest on the sum representing the present worth. The present worth is the principal, the true discount the interest, and the debt the amount. Problems coming under this head are solved, therefore, like corresponding problems in interest. PROBLEMS 205. 1. What is the present worth of a debt of $163.50, due in 1 year 6 months, at 6 %? What is the true discount? $1 + $.09 = $1.09, amount of $1 for the given time. $163.50 $1.09 $150, present worth. = $163.50 - $150 = $13.50, true discount. 2. How much must be paid now to cancel a debt of $99.45, due in 1 year 9 months, at 6 % ? 3. What is the present worth of $12,060, due in 5 years 8 months, without interest, money being worth 6 %? 4. I owe $871.50, payable in 3 years 9 months, without interest, but wish to pay it immediately. How much should be paid, money being worth 7 % ? 5. I bought two lots for $2541 on 3 years' time, without interest. What is the cash value, money being worth 7%? 6. Mr. Brown gives his note for $ 88, payable in 2 years 8 months, without interest. How much should he pay instead, at the end of 8 months, money being worth 5%? 7. A owes $6000, of which one third is to be paid in one year, and the remainder in two years. What is its present cash value, money being worth 6%? 8. I bought a store for $1500 cash, and sold it for $ 2000, one fourth to be paid in cash, the remainder in 2 yr., without interest. What was my gain, money being worth 6% ? 9. A merchant purchased $900 worth of hardware at a discount of 25%. He sold the goods at the list price on 9 months' credit. What was his gain, money being worth 6% ? 10. With money at 8%, which is more advantageous, to buy goods for $425 on 6 months' credit, or for $450 on 9 months' credit? DOMESTIC EXCHANGE 206. Exchange is the method of paying debts or collecting credits in distant places without transmission of money. Exchange between two places in the same country is called domestic exchange. Payments in the same country may be made by postal money order, by express money order, by telegraphic money order, by bank check, by bank draft, or by a commercial draft of a creditor on a debtor. A postal money order is a written order by the postmaster in one place, to the postmaster in another place, to pay a specified sum of money to the person named in the order. An express money order issued by an agent of an express company to another agent is similar to a postal money order. Both are negotiable. |