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# TAMU AGEC 330 - Homework 1 Key

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AGRICULTURAL ECONOMICS 330 Assignment 1 Instructor: Dr. David J. Leatham Key 1. Suppose you deposit \$2,500 today in a savings account at 3.5% interest compounded annually. Assuming no withdrawal, how much would you have at the end of 10 years? A. \$3,526 B. \$1,772 C. \$29,328 D. \$20,792 0 102 50010− , V r = 3.5% V10 = 2500(1+.035)10 = \$3,526.50 2. Suppose you owe a creditor \$10,000 due in a single payment in 5 years. How much should your creditor be willing to accept now if he can earn 8% on his money? A. \$14,693 B. \$39927 C. \$6,806 D. \$58,666 0 510 0000V − , r = 8% V0 = 10,000 (1 + .08)-5 = \$6,805.83 3. About how many years will it take for \$100,000 placed in a bank account at 7% interest rate compounded annually to double? (Answer = 10.24 years) A. 8.63 years B. 10.24 years C. 10 months D. 5.44 years 0100 000 200 000N− , , r = 7% 200,000 = 100,000(1+0.07)NN = 10.24 years 4. What is the approximate annual interest rate compounded annually if your money will double in 8 years if it is put in a savings account? A. 8% B. 4% C. 200% D. 9% 0 81 2− r = ? 2 = 1(1+r)8 r 9%≈ 5. Assume you borrow \$25,000 at 8% per year interest compounded annually. You pay nothing until the end of 10 years at which time the principal and interest is due. 5.1 What will be the total amount of repayment (principal and interest) at the end of the 10th year? In this problem you only make one payment; it is at the end of the 10th year. A. \$3,725 B. \$45,000 C. \$53,973.12 D. \$50,000 10000,25100V− r = 8 V10 = 25,000(1+.08)10 = \$53,973.12 5.2. How much interest is paid? A. \$53,973 B. \$28,973 C. \$20,000 D. \$25,000 53,973.12 - 25,000 = \$28,973.12 6. If you borrow \$25,000 (at 8% interest) and pay only the interest at the end of each year, what isthe total amount of principal and interest (simply add it up) over 10 years counting the \$25,000 principal which must be repaid at the end of the 10th year? A. \$45,000 B. \$2,000 C. \$20,000 D. \$28,973 Interest/year = 25,000 × .08 = 2,000 Total Interest = 2,000 × 10 = 20,000 Total Principal & Interest = 25,000 + 20,000 = \$45,000 7. Does it make any sense to compare the total (undiscounted) principal and interest on the loans from questions 5 & 6? Should you prefer the loan with the smallest total payment? Explain. A. Yes, because you always want to a loan that pays the least interest. B. No, because the time value of money was ignored in question 6. C. Yes, because in both cases the principal and interest are included. D. A and C above are correct. No, answers to #5 and #6 should not be compared. Dollars in different time periods were added together to get totals. "Time value of money" adjustments need to be made. Also, to choose the loan you prefer, your financial condition and the particular investment opportunity must be

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