a) $100 b) $250
a) b)
a) b)
MCR 3UI
Unit 7 – Day 1

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

• 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.

• 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 .

• Explain what compound interest is.
If you invest $100 and get 10% compound interest …..
100 1 + 0.10
1 = 110 .00
100 1 + 0.10
2
= 121.00
100 1 + 0.10
3 = 133.10
100 1 + 0.10
4 = 146.41
100 1 + 0.10
10 = 259.37
100 1 + 0.10
20
= 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.

• 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

• 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 interest.
𝑛 to determine the future value and the amount of a) You bought a new TV which cost $1000. 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?

• 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 of interest.
−𝑛 to determine the present value and the amount 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?

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 start 10 years
𝐴 = 𝑃 1 + 𝑖 𝑛
$1000 ???
--------------------------------------------------------------------------------------------------------------------
10. On the day his son is born, Mike wishes to invest a single sum of money that will grow to $10 000 when his son turns 21. If Mike invests the money at 4%/a compounded semiannually, how much must he invest today?
born
???
21 years
$10000
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
$10 000 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
$10000 + ???
now
$7500
𝑃 = 𝐴 1 + 𝑖
Then find total purchase price
−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
$9000
10% quarterly
3 years
???
9% semiannually
5 years (2 more)
???
𝐴 = 𝑃 1 + 𝑖 𝑛 twice

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
$2000 now
??? - 800
6 months from now
???
𝐴 = 𝑃 1 + 𝑖 𝑛 twice

Which formula to use?
Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20
16. Today Sigrid has $7424.83 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
7424.83
𝑃 = 𝐴 1 + 𝑖 twice
−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
4000
4% quarterly
???
4.2% quarterly
???
4.4% quarterly
???
𝐴 = 𝑃 1 + 𝑖 𝑛 three times

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 18 th birthday.
birth 5 years 10 years 15 years 18 years
500 ???+500 ???+ 500 ???+500 ???
𝐴 = 𝑃 1 + 𝑖 𝑛 four times