1. Calculate 10% of each number and then add it to the number
MCR 3UI Unit 7 – Day 1
Calculate 10% of each number and then add it to the number
a) $100 b) $250
Calculate 10% of answer and then add it to the answer
a) b)
Repeat the process 2 more times.
a) b)
Is there a faster way to calculate the final answers you got?

2. Monday Tuesday Wednesday Thursday Friday In-Class Assignment
Dec 17
Compound Interest
And Present Value
Dec 18
Annuities
Dec 19
More Investments
Dec 20
In-Class
Assignment
Dec 21
Finish outstanding work.
(HW for week due)
Christmas Break
Jan 7
Exponential Functions and Apps
Jan 8
Jan 9
Jan 10
Jan 11
Jan 14
Jan 15
Jan 16
Jan 17
Jan 18
Unit 7 Test
(Material from after Christmas only)
Jan 21
Exam Review
Jan 22
Jan 23
Jan 24
Period 1 Exam
Jan 25
Period 2 Exam
Jan 28
Period 3 Exam
Jan 29
MATH EXAM !!
Jan 30
Jan 31
Feb 1

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 =
672.75
If 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 years
b) 8%/a compounded semi-annually for 7 years
c) 5.5%/a compounded quarterly for 30 months
d) 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 interest
Use 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 interest
Use 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, 20
8. Find the balance of the investment if $1000 is compounded annually, at 5%/a for
(a) 10 years (b) 20 years (c) 30 years
10. 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?
start
10 years
𝐴=𝑃 1+𝑖 𝑛
$1000
???
born
21 years
𝑃=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, 20
13. 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 ago
now
𝑃=𝐴 1+𝑖 −𝑛
Then 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, 20
14. 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.
start
3 years
5 years (2 more)
10%
quarterly 9%
semiannually
$9000
???
???
𝐴=𝑃 1+𝑖 𝑛
twice

12. 𝐴=𝑃 1+𝑖 𝑛 Which formula to use?
Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20
15. 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 ago
now
6 months from now
$2000
??? - 800
???
𝐴=𝑃 1+𝑖 𝑛
twice

13. 𝑃=𝐴 1+𝑖 −𝑛 Which formula to use?
Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20
16. 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 ago
2 years ago
Today
6% semi annually
6% monthly
???
???
𝑃=𝐴 1+𝑖 −𝑛
twice

14. 𝐴=𝑃 1+𝑖 𝑛 Which formula to use?
Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20
19. 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.
now
1 year
2 years
3 years
4% quarterly
4.2% quarterly
4.4% quarterly
4000
???
???
???
𝐴=𝑃 1+𝑖 𝑛
three times

15. 𝐴=𝑃 1+𝑖 𝑛 Which formula to use?
Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20
20. 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.
birth
5 years
10 years
15 years
18 years
500
???+500
???+ 500
???+500
???
𝐴=𝑃 1+𝑖 𝑛
four times