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Name: Date: 1.1 Simple Interest YOU WILL NEED • calculator • graph paper • ruler Keep in Mind Simple interest is determined only on the principal of an investment. • The amount of simple interest earned on an investment can be determined using the formula I 5 Prt. TIP • I is the interest. • To determine the future value or amount of an investment that earns simple interest, use the formula A 5 P 1 Prt or A 5 P(1 1 rt). • P is the principal. An interest rate is assumed to be annual, or per annum (per year). • t is the time in years. Investments are described by giving • the interest rate; • r is the annual interest rate (as a decimal). • A is the future value or amount of the investment. • how and when interest is calculated, for example, simple interest calculated annually or monthly; and • the term: how long the money is invested. Example 1 Nathan invested in a $3000 guaranteed investment certificate (GIC) at 1.5% simple interest, paid annually, with a term of 5 years. How much interest will accumulate over the term of Nathan’s investment? What is the future value of his investment at maturity? Solution Step 1. I wanted to determine the accumulated interest, so I used the formula I 5 Prt. I identified the terms I knew. • The principal is $3000: P 5 3000 • The interest rate is 1.5% per annum: r 5 0.015 • The time is 5 years: t 5 5 Step 2. I substituted the values into the formula and calculated. I 5 Prt I 5 (3000)(0.015)(5) I 5 225 Nathan will accumulate $225 in interest over 5 years. 4 1.1 Simple Interest FoM12 WB_Ch01W_BLM.indd 4 TIP To convert a percent to a decimal, first think of the percent as a fraction. For example, 1.5 1.5% 5 , or 0.015. 100 NEL 7/12/12 12:04 PM Name: Date: Step 3. I know that the future value is the value of the investment at the end of the 5 years. To determine the future value, A, I added the principal and the accumulated interest. A5P1I A 5 3000 1 225 A 5 3225 The future value is $3225. Example 2 Caitlin is a co-op student. She invested her work-term earnings of $10 000 at 4% simple interest, paid annually. She intends to use the money in a few years to take a dream vacation with a friend. How long will the investment take to grow to a future value of $12 000? Determine Caitlin’s rate of return. Solution Step 1. I wanted to determine the number of years it will take $10 000 to grow to $12 000. I decided to use the formula A 5 P 1 Prt and solve for t. • The principal is $10 000: P 5 10 000 • The rate of interest is 4% per annum: r 5 0.04 • The future value is $12 000: A 5 12 000 Step 2. I substituted and then solved for t. A 5 P 1 Prt 12 000 5 10 000 1 (10 000)(0.04)t 2000 5 400t 2000 5t 400 55t The value of the investment will be $12 000 in 5 years. Step 3. I calculated the interest earned. Interest earned: future value 2 principal 5 $12 000 2 $10 000, or $2000 Step 4. I determined the rate of return. TIP interest earned Rate of return 5 amount invested Rate of return 5 2000 10 000 Determine the rate of return as the ratio of money earned to the amount of money invested. Rate of return 5 0.2 The rate of return is 20% over 5 years. NEL FoM12 WB_Ch01W_BLM.indd 5 1.1 Simple Interest 5 7/12/12 12:04 PM Name: Date: Practice 1. Rahim invests $250 at 3.5% simple interest for 3 years. a) Determine the interest earned on Rahim’s investment. b) Determine the future value of Rahim’s investment. c) Determine Rahim’s rate of return. 2. Paula invested her summer earnings of $3000 at 2.4% simple interest, paid annually. She will use the money in a few years to help with university expenses. a) How long will it take for the future value of the investment to grow to $3500? Round your answer to the nearest year. TIP For the rate of return, use the actual value at the end of the year when the investment is worth at least $3500, not the desired value of exactly $3500. b) Determine Paula’s rate of return, to the nearest tenth of a percent. 3. When Jeremy was born, his grandmother invested $1500 at 3% simple interest, paid annually. The money is to be used for school expenses. a) How long will it take for the future value of the investment to grow to $2000? Round your answer up to the nearest year. TIP Round the number of years up in this case, because interest is not paid until the end of each year. b) Determine the rate of return, to the nearest tenth of a percent. 4. A principal of $800 000 is invested at 3.4% simple interest, paid annually, for 5 years. What is the rate of return? 6 1.1 Simple Interest FoM12 WB_Ch01W_BLM.indd 6 NEL 7/12/12 12:04 PM Name: Date: 5. A principal of $16 500 is invested at simple interest for 15 years and grows to a future value of $22 000. a) Determine the interest rate. Round your answer to the nearest tenth of a percent. TIP Interest rates are almost always quoted per year, but sometimes they are calculated more frequently. b) Determine the rate of return, to the nearest tenth of a percent. MULTIPLE CHOICE 6. $270 is invested at 1.25% simple interest for 6 years. Interest is paid weekly. Determine the interest earned. A. $202.50 B. $3.38 C. $20.25 D. $270.25 7. Audrey invested $60 000 at 1.9% simple interest. At the investment’s maturity, its value was $62 280. For how long was the money invested, and what was the rate of return? A. 1 year, 1.9% B. 2 years, 1.9% C. 1 year, 3.8% D. 2 years, 3.8% 8. Aiden invested $435 at simple interest for 3 years. At the investment’s maturity, its value was $572.03. What was the rate of interest, and what was the rate of return? A. 1.05%, 20% B. 20%, 10.5% C. 10.5%, 20% D. 12%, 15% WRITTEN RESPONSE 9. Amelia deposits $500 into a savings account that earns 3% simple interest, for 2 years. On the same day, her brother Caleb deposits $200 into a savings account that earns 5% simple interest, for 3 years. Who will earn more interest? Who has the greater rate of return? Provide a complete solution. NEL FoM12 WB_Ch01W_BLM.indd 7 1.1 Simple Interest 7 7/12/12 12:04 PM