Presentation on theme: "Calculate 10% of each number and then add it to the number"— Presentation transcript:
1 Calculate 10% of each number and then add it to the number MCR 3UI Unit 7 – Day 1Calculate 10% of each number and then add it to the numbera) $100 b) $250Calculate 10% of answer and then add it to the answera) b)Repeat the process 2 more times.a) b)Is there a faster way to calculate the final answers you got?
3 Unit 7 – Day 1: Compound Interest and Present Value Explain what compound interest is.Determine the future value of an investment/loan and the amount of interest earned.Determine the present value of an investment/loan and the amount of interest earned.
4 For the right to use your money they pay you. Explain what compound interest is.If you invest money in a bank (or many other types of investments) then the bank can use your money.For the right to use your money they pay you.They usually pay you a percentage of the money you invest.This payment is known as interest.The money you originally invested in known as the principal.If you borrow money from a bank or do not pay for something right away then you must (usually) pay extra money for this right/ability.This charge is also known as interest.
5 If you invest $100 and get 10% compound interest ….. Explain what compound interest is.If you invest $100 and get 10% compound interest …..=110.00=121.00=133.10=146.41=259.37=672.75If you invest $100 and get 10% not compound interest …..With compound interest your money grows faster because you get interest on the interest.
6 Example 1: Number of compounding periods and interest per period. Explain what compound interest is.Example 1: Number of compounding periods and interest per period.Determine the number of compounding periods and the interest per period.a) 5%/a compounded annually for 10 yearsb) 8%/a compounded semi-annually for 7 yearsc) 5.5%/a compounded quarterly for 30 monthsd) 9.4%/a compounded monthly for 26 weeks
7 Example 2: Determining the future value and the amount of interest Determine the future value of an investment/loan and the amount of interest earned.Example 2: Determining the future value and the amount of interestUse the formula 𝐴=𝑃 1+𝑖 𝑛 to determine the future value and the amount of interest.a) You bought a new TV which cost $ You were given the option to defer your payment for 2 years with interest of 6%/a compounded monthly. How much will you owe in 2 years? What amount of interest will you be charged?b) Suppose you made a down payment of $400. How much less interest would you be charged?c) Suppose interest was 7%/a compounded quarterly and you only waited 18 months to pay. (No down payment) How much would you owe?
8 Example 3: Determining the present value and the amount of interest Determine the present value of an investment/loan and the amount of interest earned.Example 3: Determining the present value and the amount of interestUse the formula 𝑃=𝐴 1+𝑖 −𝑛 to determine the present value and the amount of interest.a) You want to have $15,000 saved for your first year of school. How much would you need to invest now if you want to go to school in 3 years and interest is 4%/a compounded annually. How much interest would you earn?b) Suppose interest was 4%/a compounded monthly. Would you earn more or less interest? How much more/less?c) Suppose the money had been invested when you were 5 years old and you planned to go to school at the age of 18. If interest was 4%/a compounded annually how money would you have needed to invest? How much interest would you have earned?
9 𝐴=𝑃 1+𝑖 𝑛 𝑃=𝐴 1+𝑖 −𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 208. Find the balance of the investment if $1000 is compounded annually, at 5%/a for(a) 10 years (b) 20 years (c) 30 years10. On the day his son is born, Mike wishes to invest a single sum of money that will grow to $ when his son turns 21. If Mike invests the money at 4%/a compounded semiannually, how much must he invest today?start10 years𝐴=𝑃 1+𝑖 𝑛$1000???born21 years𝑃=𝐴 1+𝑖 −𝑛???$10000
10 𝑃=𝐴 1+𝑖 −𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 2013. Barry bought a boat two years ago and at that time paid a down payment of $ cash. Today he must make a second and final payment of $7500, which includes the interest charge on the balance owing. Barry financed this purchase at 6.2%, compounded semiannually. Determine the purchase price of the boat.2 years agonow𝑃=𝐴 1+𝑖 −𝑛Then find total purchase price$ ???$7500
11 𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 2014. Tiffany deposits $9000 in an account that pays 10%/a compounded quarterly. After three years, the interest rate changes to 9%/a compounded semiannually. Calculate the value of her investment two years after this change.start3 years5 years (2 more)10%quarterly9%semiannually$9000??????𝐴=𝑃 1+𝑖 𝑛twice
12 𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 2015. Exactly six months ago, Lee borrowed $2000 at 9% compounded semiannually. Today he paid $800, which included principal and interest. What must he pay to close the debt at the end of the year (six months from now)6 months agonow6 months from now$2000??? - 800???𝐴=𝑃 1+𝑖 𝑛twice
13 𝑃=𝐴 1+𝑖 −𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 2016. Today Sigrid has $ in her bank account. For the last two years, her account has paid 6%/a, compounded monthly. Before then, her account paid 6%/a, compounded semiannually, for four years. If she made only one deposit six years ago, determine the original principal.6 years ago2 years agoToday6% semi annually6% monthly??????𝑃=𝐴 1+𝑖 −𝑛twice
14 𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 2019. Bernie deposited $4000 into the “Accumulator Account” at his bank. During the first year, the account pays 4%/a, compounded quarterly. As an incentive to the bank’s customers, this account’s interest rate in increased by 0.2% each year. Calculate the balance in Bernie’s account after three years.now1 year2 years3 years4% quarterly4.2% quarterly4.4% quarterly4000?????????𝐴=𝑃 1+𝑖 𝑛three times
15 𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 2020. On the day Sarah was born, her parents deposited $500 in a savings account that earns 4.8%/a, compounded monthly. They deposited the same amount on her 5th, 10th, and 15th birthdays. Determine the balance in the account on Sarah’s 18th birthday.birth5 years10 years15 years18 years500???+500???+ 500???+500???𝐴=𝑃 1+𝑖 𝑛four times