Lesson 2: Compound Interest (Future Value)
Part A – Definitions/Introduction
 compound interest: Interest that is added to the principal before new interest
earned is calculated. So interest is calculated on the principal and on interest
already earned.
 compounding period: regular time intervals that interest is calculated and then
paid. For example,
o annually (1 time per year)
o semi-annually (2 times per year)
o quarterly (4 times per year)
o monthly (12 times per year)
o daily (365 times per year)
Part B – Formula to Calculate the Amount (Future Value)
A = P (1+i)n
where;
A – is the amount or future value of an investment or loan
P – is the original principal invested or borrowed
i – is the interest rate per compounding period
n – is the total number of compounding period
Part C – Determining i and n
Determine i and n for each:
a) 5%/a compounded annually for 4 years
b) 6%/a compounded semi-annually for 10 years
c) 8%/a compounded quarterly for 2 years
Rate per
Compounded
annum, % (Frequency)
Compounding Rate per
Periods in one Compounding
year
Period, i %
( annual rate
# of
compounding periods
in a year)

5
annually
6
semi-annually
8
quarterly
Term
(years)
Number of
Compounding
Periods, n
(# of years
# of compounding
periods in a year)

Part D – Determining the Amount
Consider…. What effect does more frequent compounding have? Any guesses?
Let’s find out!!!
Example :
Eric has four options to invest $10 500 in a 3-year GIC (guaranteed investment
certificate) at 3.5%/a.
a) Determine the amount at the end of the three years if the interest is compounded
(i) annually, (ii) semi-annually, (iii) quarterly, or (iv) monthly.
(i) Annually:
(ii) Semi-annually:
(iii) Quarterly:
(iv) Monthly:
Conclusion: The more frequent the compounding,
b) Calculate Eric’s total interest earned in option (iii) above. (Recall: A = P + I )
Part E – Comparing Compound Interest and Simple
Interest
Recall the previous lesson where $1 000 was invested at 5%/a earning simple
interest for 10 years. Each year an additional $50 of interest was earned. This
simulated an arithmetic sequence and when graphed it indicated linear growth.
(i)
Consider the same investment but the interest is now compounded
annually.
No. of Years
Principal ($)
P
Interest Rate
i=r
1
2
1 000
0.05
Interest ($)
I
50
Amount ($)
A
1 050
(ii)
Plot the points in the table the points in the table from (i), with the time,
in years, along the horizontal axis and the amount, in dollars, along the vertical
axis. Join the points.
(iii)
Consider the values in the Amount column. What kind of sequence do you
notice? Explain.