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Unformatted text preview: Math 006 (Lecture 1) Simple Interest
Deﬁnition 1. Let r be the annual interest rate. Suppose we deposit/borrow a sum of money P in/from a bank, then after t years, the amount you will receive/pay, A, is given by A = P + I = P + P rt = P (1 + rt) where I is the interest received/owed. The principal, P , is often referred to as the present value and A as the future value. Example 1. Find the total amount due on a loan of $1000 at 6% simple interest rate at the end of (a) 2 years; (b) 4 months. Example 2. If you want to earn an annual rate of 20% on your investments, how much should you pay for a note that will be worth $5,000 in 9 months? Example 3. T-bills (Treasury bill) are one of the instruments the U.S. Treasury Department uses to ﬁnance the public debt. If you buy a 180-day T-bill with a maturity value of $10,000 for $9800, what annual simple interest rate you will earn? 1 Example 4. You sell an old car to our friend and accept a 270-day note for $3,500 at 10% simple interest rate as payment. (Both principal and interest will be paid at the end of 270 days.) Sixty days later you ﬁnd the you need the money and sell the note to a third party for $3,550. What annual interest rate will the third party receive for the investment? Example 5. The brokerage ﬁrm charge commissions based on the amount of the trade. The following table shows the commission schedule for one of these ﬁrms. Transaction Size $0-$2,499 $2,500-$9,999 $10,000+ Commission $29+1.6% of principal $49+0.8% of principal $99+0.3% of principal An investor purchases 50 shares of a stock at $47.52 per share. After 200 days, the investor sells the stock for $52.19per share. Using the above commission schedule, ﬁnd the annual rate of interest earned by this investment. 2 ...
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