E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is


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1 E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t = (half a year), for 1 month use t = = For 3 months use t =. For 1 day use t =. NOTE: Per annum means. It is sometimes written as p.a. EXAMPLE: What is the simple interest on 5% p.a. for 3 years? What is the total amount after this time? SOLUTION: Simple Interest = The total amount is Total Amount =
2 QUESTIONS FOR STUDENTS: Students should do INVESTIGATION 1: Simple Interest on page 250 from the text. In each part of this Investigation students should write down what they multiply to get their answers. Students should also calculate the Total Amount for each calculation. Fill in the answers below: 1. 1 year Interest Total Amount 2. 2years Interest Total Amount 5years 10years Interest Total Amount Interest Total Amount 3. 6months Interest Total Amount 3months 1month Interest Total Amount Interest Total Amount 4. 40days Interest Total Amount
3 COMPOUND INTEREST With Compound Interest the interest is added onto the principal after every calculation period. Look at the example below. EXAMPLE: What is the Total Amount earned if $1000 is invested at 8% p.a. compounded 4 times a year for 1 year? What is the Interest? NOTE: 8% per year must be considered as per period. Fill in the table below: Period Principal 1 Rate per period 2% Interest Amount ANSWER: The Amount after 1 year is. The Interest must be NOTICE: a) b) c) d)
4 QUESTIONS FOR STUDENTS 1. Give the rate per period and the decimal to be used for the following: (The first one is done for you.) a) 12%, 4 times a year Rate per period 12/4 = 3% Decimal 0.03 b) 16%, 2 times a year Rate per period Decimal c) 6%, 3 times a year Rate per period Decimal d) 10%, 4 times a year Rate per period Decimal e) 5%, 4 times a year Rate per period Decimal f) 10%, 12 times a year Rate per period Decimal g) 10%, every month Rate per period Decimal 2. Calculate the number of periods for the following: The first is done for you. a) 4 times a year for 6 years Number of periods 4 x 6 = 24 b) 12 times a year for 2 years Number of periods c) 3 times a year for 4 years Number of periods d) Twice a year for 8 years Number of periods e) Every month for 5 months Number of periods f) Every month for 5 years Number of periods g) Every day for 1 year Number of periods NOTE: There are special names given for certain periods. Every three months = 4 times a year is called QUARTERLY Every six months = 2 times a year is called SEMIANNUALLY Every year once a year is called ANNUALLY Every month = 12 times a year is called MONTHLY
5 3. Fill in the following tables to calculate the Amount and Interest for the following questions. (Follow the example from compound interest.) a) Invest 12% p.a. compounded 2 times a year (semiannually) for 2 years. Period Principal Rate 6% Interest Amount Amount Interest b) Invest $ 10 12% p.a. compounded quarterly for 1 year. Period Principal Rate Interest Amount Amount Interest c) Invest $ % p.a. compounded monthly for 5 months Period Principal Rate Interest Amount Amount Interest
6 E INV 2 AM11 COMPOUND INTEREST USING THE FORMULA Name: COMPOUND INTEREST FORMULA: There is a compound interest formula which calculates the amount directly. A = P = r = n = t = The value of n The value of t Annually n = For time given in years Semiannually n = For time given in months Quarterly n = For time given in days Monthly n = Daily n =
7 EXAMPLE 1: Use the formula to calculate the Amount and Interest for an investment of 6% p.a. compounded quarterly (4 times a year) for 2 years. SOLUTION: In this example: P = The rate is 6% p.a. so r = Compounded quarterly so n = The time in years is 2 years so t = The Amount = To get the answer press the following: This comes to ANSWER: The Amount is The Interest is EXAMPLE 2: Find the amount and interest using the compound interest formula for an investment of $ compounded semiannually at 8% p.a. for 18 months. SOLUTION: In this example: P = The rate is 8% p.a. so r = Compounded semiannually so n = The time in years is 18 months so t = The Amount = To get the answer press the following: This comes to ANSWER: The Amount is The Interest is
8 QUESTIONS FOR STUDENTS Use the formula A = P ( 1 + r/n) nt to calculate the following: Principal Rate p.a. 1. $2500 4% Time Compounded Amount Interest 3 years Annually r = 2. $3500 5% r = 3. $ % r = 4. $ % r = 5. $ % r = 6. $ % r = 7. $ % r = 8. $ % r = 9. $ % t = 2 years t = 2 years t = 10 years t = 2 years t = 30 days t = 6 months t = 9 months t = 6 months n = Semiannually n = Monthly n = Quarterly n = Daily n = Daily n = Monthly n = Semiannually n = Monthly 10. $ r = 8% r = t = 1 day t = n = Daily n =
9 FURTHER QUESTIONS Calculate the Amount and Interest for the following: a) 10% p.a. compounded semiannually for 5 years Amount Interest b) $10 8% p.a. compounded quarterly for 3 years Amount Interest c) 10% p.a. compounded monthly for 6 years Amount Interest d) 10% p.a. compounded semiannually for 12 years Amount Interest e) $ % p.a. compounded monthly for 1 month (hint 1 month = 1/12 years) Amount Interest
10 E INV 3 AM11 Name: INVESTMENTS EXAMPLES: 1. Find the amount and interest if $ is 8% p.a. for 5 years compounded annually 2. Find the amount and interest if $ is 8% p.a. for 5 years compounded semiannually 3. Find the amount and interest if $5 000 is 12 % p.a. for 5 months compounded annually 4. Find the amount and interest if $4 500 is 12 % p.a. for 9 months compounded semiannually 5. Find the amount and interest if $8 000is 7.8 % p.a. for 60 days compounded semiannually. 6. Find the amount and interest if $ is 9.5 % p.a. for 7 days compounded daily
11 PRACTICE QUESTIONS 1. Find the amount and interest if $ is 5% p.a. for 6 years compounded annually Amount Interest 2. Find the amount and interest if $ is 5% p.a. for 6 years compounded semiannually Amount Interest 3. Find the amount and interest if $ is 5% p.a. for 6 years compounded quarterly Amount Interest 4. Find the amount and interest if $ is 5% p.a. for 6 years compounded monthly Amount Interest 5. Find the amount and interest if $ is 5% p.a. for 6 years compounded daily Amount Interest 6. Find the amount and interest if $ is 8% p.a. for 5 months compounded semiannually Amount Interest 7. Find the amount and interest if $ is 8% p.a. for 5 months compounded monthly Amount Interest 8. Find the amount and interest if $ is 8% p.a. for 5 months compounded daily Amount Interest 9. Find the amount and interest if $ is 8% p.a. for 10 days compounded semiannually Amount Interest 10. Find the amount and interest if $ is 8% p.a. for 10 days compounded daily Amount Interest
12 CALCULATING TIMES FOR INVESTMENTS EXAMPLES: 1. How long for $1000 to reach $1200 at 7% p.a. compounded semiannually? 2. How long for $1000 to reach $1200 at 7% p.a. compounded monthly? PRACTICE: 1. How long for $3000 to reach $4200 at 6% p.a. compounded MONTHLY? 2. How long for $1000 to reach $2000 at 5% p.a. compounded SEMIANNUALLY? 3. How long for $5000 to reach $6700 at 8% p.a. compounded MONTHLY? 4. How long for $1000 to reach $1200 at 7% p.a. compounded DAILY? 5. How long for $1000 to DOUBLE at 7% p.a. compounded MONTHLY?
13 CALCULATING RATES FOR INVESTMENTS EXAMPLE: What rate is needed for $1000 to reach $1200 if it is compounded semiannually for three years? PRACTICE 1. What rate is needed for $1500 to reach $2500 if it is compounded semiannually for five years? 2. What rate is needed for $2000 to reach $4000 if it is compounded monthly for three years? 3. What rate is needed for $3000 to reach $4000 if it is compounded annually for four years? 4. What rate is needed for $ to reach $ if it is compounded quarterly for six years?
14 E INV 5 AM11 Name: INVESTMENTS: FURTHER QUESTIONS EXAMPLE A: Lump Sum Find the time taken Determine the time taken for an investment of 9.3% p.a. compounded monthly to double in value. Answer in years. ANNUITIES Determine the final amount for an investment of $200 paid at the end of every 6% p.a. compounded quarterly for 2 years. Period TOTAL
15 ANNUITY FORMULA: There is an anuuity formula which calculates the amount directly. A = R = i = n = t = Annuity Find the monthly payment Determine how much you would need to pay twice a 7% p.a. compounded semiannually to save $ in 20 years. A: Lump Sum Investment. Find the time taken in years. 1. Determine the time taken for an investment of 5.3% p.a. compounded monthly to reach $ Determine the time taken for an investment of $10 4.5% p.a. compounded semiannually to reach $ Determine the time taken for an investment of 7.5% p.a. compounded quarterly to reach $ Determine the time taken for an investment of 5.5% p.a. compounded monthly to double in value. Answer in years.
16 B: Annuities. Determine the final amount. 5. Determine the final amount for an investment of $300 paid at the end of every 5% p.a. compounded semiannually for 3 years. 6. Determine the final amount for an investment of $100 paid every 7.5% p.a. compounded quarterly for 5 years. 7. Determine the final amount for an investment of $250 paid every 8% p.a. compounded monthly for 2 years. 8. Determine the final amount for an investment of $200 paid 6% p.a. compounded semiannually for 3 years. 9. Determine the final amount for an investment of $200 paid at the start of every 4.5% p.a. compounded semiannually for 2 years. 10. Determine the final amount for an investment of $300 paid 7.6% p.a. compounded semiannually for 6 years. C: Calculate regular payments. Determine the payment. 11. Determine how much you would need to pay each 7% p.a. compounded monthly to save $ in 10 years. 12. Determine how much you would need to pay each 8% p.a. compounded annually to save $5 000 in 5 years. 13. Determine how much you would need to pay at the end of each 9% p.a. compounded monthly to save $ in 6 years. 14. Determine how much you would need to pay twice a 10% p.a. compounded semiannually to save $6 000 in 3 years. 15. Determine how much you would need to pay 7.5% p.a. compounded quarterly to save $ in 4 years. 16. Determine how much you would need to pay each 5% p.a. compounded monthly to save $ in 25 years.
17 E INV 8 AM 11 Name: Investments PRACTICE QUESTIONS 1. to calculate the amount (Future Value) of the following investments: a) $1000 invested at 6% per annum compounded semiannually for 5 years. b) $ 800 invested at 4.8% per annum compounded semiannually for 3 years c) $ 600 invested at 8% per annum compounded quarterly for 3 years. d) $1200 invested at 6.8% per annum compounded quarterly for 10 years. e) $2500 invested at 12% per annum compounded monthly for 4 years. f) $ invested at 5.4% per annum compounded monthly for 8 years. 2. Determine the following times. Answer in years. a) How long will it take an investment of $1 000 to reach $1 200 at 6.5% p.a. compounded monthly? Answer in years. b) How long will it take an investment of $35 paid at the end of each month at 6.5% p.a. compounded monthly to reach $ Determine the following times. Answer in years. a) How long will it take for an investment of $5 000 at 5.6% p.a. compounded quarterly to double in value? b) How long will it take for an investment of $ at 9.5% p.a. compounded semiannually to triple in value? c) How long will it take for an investment of $3 000 at 8.2% p.a. compounded annually to reach $5 000? 4. to find the future value for the following: a) A bank offers an interest rate of 10% p.a. compounded annually. Pay $2400 at the end of each year for three years. b) A bank offers an interest rate of 5.7% p.a. compounded quarterly. Pay $500 invested at the end of each quarter for two years. c) A bank offers an interest rate of 6.8% p.a. compounded monthly. Invest $ 100 every month for ten years. d) Invest $200 every month at an interest rate of 8% p.a. compounded monthly for 20 years. 5. Determine the following times a) How long will it take an investment of $500 paid each month at 6 % p.a. compounded monthly to reach $ ? b) How long will it take an investment of $500 paid each month at 12 % p.a. compounded monthly to reach $ ? c) How long will it take an investment of $200 paid each month at 9.5 % p.a. compounded monthly to reach $ ?
18 6. Determine: a) What amount must be invested monthly from age 20 to age 55 at 8.5% p.a. compounded monthly in order to accumulate $ ? b) What amount must be invested quarterly from age 20 to age 60 at 6.4% p.a. compounded quarterly in order to accumulate $ ? c) What amount must be invested daily from age 20 to age 55 at 7.4% p.a. compounded daily in order to accumulate $ ? 7. Determine: a) When you are born, your parents invest $50 a month at 6.8% p.a. compounded monthly in a nontaxable Registered Education Savings Plan for your college education. How much will be accumulated by the time you reach 18? b) When you are born, your parents invest $2 a day in an RRSP at 8% p.a. compounded daily for you. How old will you be when you have $10 000?
19 E LN 1 AM11 INTRODUCTION TO LOANS Name: 1. What is the monthly payment on a loan of $1000 at 8% p.a. compounded annually for 4 years? What is the total cost of the loan? What is the finance charge? Period TOTAL Monthly Payment Total Cost of Loan Finance Charge _ 2. What is the semi annual payment on a loan of $2000 at 5% p.a. compounded semiannually for 5 years? What is the total cost of the loan? What is the finance charge? Period Monthly Payment Total Cost of Loan Finance Charge
20 LOAN FORMULA: There is a loan formula which calculates the amount directly. P = R = i = n = t =
21 E LN 2 AM11 Name: LOANS PRACTICE QUESTIONS Calculate the payment, the total paid and the finance charge for the following: 1. $ 5000 loan paid 7.5% p.a. compounded monthly for 6 years Payment Total Paid Finance Charge 2. $ 8000 loan paid 4.5% p.a. compounded semiannually for 4 years Payment Total Paid Finance Charge 3. $ 2000 loan paid 8.5% p.a. compounded quarterly for 3 years Payment Total Paid Finance Charge 4. $ 5000 loan paid 5% p.a. compounded semiannually for 5 years Payment Total Paid Finance Charge
22 5. $ 7000 loan paid 6% p.a. compounded quarterly for 3 years Payment Total Paid Finance Charge 6. $ loan paid 7% p.a. compounded semiannually for 10 years Payment Total Paid Finance Charge 7. $ loan paid 7.5% p.a. compounded annually for 20 years Payment Total Paid Finance Charge 8. $ loan paid 5.5% p.a. compounded semiannually for 25 years Payment Total Paid Finance Charge
23 E LN 3 AM11 Name: MORE LOANS Example 1: What interest rate compounded monthly is needed for a loan of $5 000 to be paid off over 3 years with regular payments of $150 per month? Example 2: How long is needed for a $4 000 loan compounded monthly at 5.8% to be paid off with payments of $80 per month? PRACTICE: 1. What interest rate compounded monthly is needed for a loan of $8 000 to be paid off over 6 years with regular payments of $160 per month? 2. What interest rate compounded monthly is needed for a loan of $4 000 to be paid off over 4 years with regular payments of $90 per month? 3. What interest rate compounded monthly is needed for a loan of $5 000 to be paid off over 5 years with regular payments of $100 per month? 4. What interest rate compounded monthly is needed for a loan of $4 500 to be paid off over 3 years with regular payments of $130 per month? 5. What interest rate compounded quarterly is needed for a loan of $3 000 to be paid off over 5 years with regular payments of $60 per quarter? 6. How long is needed for a $5 000 loan compounded monthly at 8 % to be paid off with payments of $100 per month? 7. How long is needed for a $3 000 loan compounded monthly at 6.2% to be paid off with payments of $200 per month? 8. How long is needed for a $ loan compounded monthly at 10.5% to be paid off with payments of $200 per month? 9. How long is needed for a $ loan compounded quarterly at 5.8% to be paid off with payments of $800 quarterly? 10. How long is needed for a $4 000 loan compounded semiannually at 7.5% to be paid off with payments of $400 semiannually?
24 E LN 5a AM 11 Practice BUYING CARS Name: New Cars: The tax is Used Cars: The tax is EXAMPLE: 1. You wish to buy a new car for $ You trade in your old car for $ The dealership offers a loan for 2% p.a. to be paid monthly over 4 years, compounded semiannually. a. What is the tax on the new car? What is the total cost of the new car? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 4 years? e. What is the finance charge? PRACTICE: 1. You wish to buy a new car for $ You trade in your old car for $ The dealership offers a loan for 1.5% p.a. to be paid monthly over 5 years, compounded semiannually. a. What is the tax on the new car? What is the total cost of the new car? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 5 years? e. What is the finance charge?
25 2. You wish to buy a new car for $ You trade in your old car for $ The dealership offers a loan for 0.9 % p.a. to be paid monthly over 4 years, compounded semiannually. a. What is the tax on the new car? What is the total cost of the new car? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 4 years? e. What is the finance charge? 3. You wish to buy a new car for $ You trade in your old car for $ The dealership offers a loan for 1.8% p.a. to be paid monthly over 3 years, compounded semiannually. a. What is the tax on the new car? What is the total cost of the new car? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 3 years? e. What is the finance charge?
26 4. You wish to purchase a used car for $ You have a $3 000 downpayment. You borrow from the bank at 6.8% to be paid monthly over 5 years, compounded semiannually. a. What is the tax on the car you wish to purchase? What is the total cost? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 5 years? e. What is the finance charge? 5. You wish to purchase a used car for $ You have a $1 000 downpayment. You borrow from the bank at 8.8% to be paid monthly over 3 years, compounded semiannually. a. What is the tax on the car you wish to purchase? What is the total cost? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 3 years? e. What is the finance charge?
27 6. You wish to purchase a used car for $ You have a $4 000 downpayment. You borrow from the bank at 7.5% to be paid monthly over 4years, compounded semiannually. a. What is the tax on the car you wish to purchase? What is the total cost? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 4 years? e. What is the finance charge? 7. You wish to purchase a used car for $ You have no downpayment. You borrow from the bank at 5.5% to be paid monthly over 2 years, compounded semiannually. a. What is the tax on the car you wish to purchase? What is the total cost? b. What is the amount borrowed? c. What is the monthly payment? d. What is the total payment over 2 years? e. What is the finance charge?
28 E LN 6a AM 11 Name: BUYING A HOUSE DEFINITIONS: 1. Mortgage (p.434) 2. Downpayment (own words) 3. Amortization Period (p.423) 4. Annuity (p.264) 5. Fair Market Value (p.430) 6. Assessed Value (p.237) 7. Mill Rate (p.434) 8. Property Tax (p.237)
29 EXAMPLE: The fair market value for a house is $ You have a minimum downpayment of 10% of the fair market value. The assessed value of the house is 80% of the fair market value. The mill rate is 20 mills. Calculate the following: a) The downpayment b) The amount of the mortgage c) The monthly payment at 6.8% p.a. compounded semiannually for 25 years d) The annual property tax e) The amount needed each month to cover the tax f) The total needed each month for mortgage plus property taxes g) The amount owing (balance) after 10 years h) The finance charge over 25 years i) The monthly payment on the original loan if the mortgage was taken out for 15 years instead of 25 years. j) The finance charge over 15 years
30 PRACTICE 1. The fair market value for a house is $ You have a minimum downpayment of 25% of the fair market value. The assessed value of the house is 80% of the fair market value. The mill rate is 25 mills. Calculate the following: a) The downpayment b) The amount of the mortgage c) The monthly payment at 5.5% p.a. compounded semiannually for 25 years d) The annual property tax e) The amount needed each month to cover the tax f) The total needed each month for mortgage plus property taxes g) The amount owing (balance) after 10 years h) The finance charge over 25 years i) The monthly payment on the original loan if the mortgage was taken out for 15 years instead of 25 years. j) The finance charge over 15 years
31 2. The fair market value for a house is $ You have a minimum downpayment of 15% of the fair market value. The assessed value of the house is 85% of the fair market value. The mill rate is 22 mills. Calculate the following: a) The downpayment b) The amount of the mortgage c) The monthly payment at 6.5% p.a. compounded semiannually for 25 years d) The annual property tax e) The amount needed each month to cover the tax f) The total needed each month for mortgage plus property taxes g) The amount owing (balance) after 10 years h) The finance charge over 25 years i) The monthly payment on the original loan if the mortgage was taken out for 15 years instead of 25 years. j) The finance charge over 15 years
32 E LN 6b Name: MORTGAGES EXAMPLE: You wish to borrow $ to buy a house. Calculate the monthly payment, the total borrowed, and the finance charge for an interest rate of 7% p.a. compounded monthly over 25 years. Monthly payment Total Amount Finance Charge A. Investigate what happens when the interest rate is changed If the same mortgage of $ is taken out at 7.5% p.a. compounded monthly for 25 years, give the monthly payment, total amount, and finance charge. Monthly payment Total Amount Finance Charge How much do you save on your monthly payment at 7% instead of 7.5% p.a.? How much do you save on your finance charge at 7% instead of 7.5% p.a.? B. Investigate what happens when the years of the mortgage is changed If the same mortgage of $ is taken out at 7% p.a. compounded monthly for 10 years, give the monthly payment, total amount, and finance charge. Monthly payment Total Amount Finance Charge How much do you save on the monthly payment if the time is 25 years instead of 10 years? How much do you save on your finance charge if the time is 10 years instead of 25 years? All mortgages are paid monthly and compounded monthly
33
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