The document discusses credit card interest rates and how to calculate effective interest rates. It provides examples of calculating future values of investments with different interest rates compounded at various time periods, from daily to annually. The rule of 72 is introduced as a way to estimate doubling time for investments based on the interest rate.

1. Credit Cards and Interest
Rates
current Canadian rates
My favorite Credit Card by flickr user .KM.

2. Solve for FV (the future value) ...
You decide to invest $6500. The bank offers an interest rate of
8.25% compounded annually. What will your money be worth in 7
years if the interest rate remains unchanged?
HOMEWORK
N=
I%=
PV=
PMT=
FV=
P/Y=
C/Y=
PMT: END BEGIN

3. HOMEWORK
Watching Money Grow ...
N=
Calculate the final balance I%=
if $7500 were invested at PV=
8% per year, compounded PMT=
semi-annually for 6 years. FV=
P/Y=
C/Y=
PMT: END BEGIN
How long will it take $12 000
N=
invested at 7.2% per year,
I%=
compounded quarterly, to
PV=
grow to $15 000?
PMT=
FV=
P/Y=
C/Y=
PMT: END BEGIN

4. Investing Regularly ... HOMEWORK
N=
Calculate the final balance if $1500 were
I%=
invested at 8% per year, compounded semi-
PV=
annually, with additional investments of $1 000
PMT=
at the end of every six months for five years.
FV=
P/Y=
C/Y=
PMT: END BEGIN
How long will it take to save $35 000, if $2 500 N=
were invested at 7.2% per year, compounded I%=
quarterly, followed by an additional $400 at the PV=
end of each 3-month period? PMT=
FV=
P/Y=
C/Y=
PMT: END BEGIN

5. Investing Frequently ...
A financial institution offers an annual interest rate of 6%,
compounded monthly.
Compare $1200 invested at the end of each year to $100 invested
at the end of each month.
Option 2: $100/month
Option 1: $1200/year
N=
N=
I%=
I%=
PV=
PV=
PMT=
PMT=
FV=
FV=
P/Y=
P/Y=
C/Y=
C/Y=
PMT: END BEGIN
PMT: END BEGIN

6. Doubling Our Money ...
$1200 is invested at 6% interest compounded annually. How long
will it take to double?
N=
N=
I%=
I%=
PV=
PV=
PMT=
PMT=
FV=
FV=
P/Y=
P/Y=
C/Y=
C/Y=
PMT: END BEGIN
PMT: END BEGIN

7. The Rule of 72
Here's a handy way to figure out how long your investment will take to
double in value. It is called the Rule of 72.
(Interest Rate %) x (Years to Double) = 72
To find the number of years given a percentage:
Years = 72
(Interest Rate %)
To find the percentage required to double given the years:
Rate = 72
Years
Numbers 72 by flickr user szczel

8. Scenario 1: You have an investment that compounds annually at
7%. How long will it take to double?
Scenario 2: You are shopping for an investment that will double in
6 years. What interest rate are you looking for?

9. Use the Rule of 72 to estimate the doubling time for these interest rates:
(c) 24% per annum,
(b) 8% per annum,
(a) 4% per annum,
compounded annually
compounded annually compounded annually
Use the TVM solver in your calculator to calculate the the compound
amount of a $100 investment for the doubling times estimated above.
N= N= N=
I%= I%= I%=
PV= PV= PV=
PMT= PMT= PMT=
FV= FV= FV=
P/Y= P/Y= P/Y=
C/Y= C/Y= C/Y=
PMT: END BEGIN PMT: END BEGIN PMT: END BEGIN
How accurate does the Rule of 72 seem to be?

10. Understanding Credit
Card Interest Rates
or
The Difference Between
Nominal and
Effective Interest Rates
Credit Cards by flickr user Andres Rueda

11. Nominal vrs. Effective Interest Rate
You have money to invest in interest-earning deposits. You have
determined that suitable deposits are available at your bank paying
6.5% per annum compounded annually, at a local trust company paying
6.4% per annum compounded monthly and at the Student Credit Union
paying 6.45% per annum compounded semiannually. Which institution
offers the best rate of interest?
N=
N= N=
I%=
I%= I%=
PV=
PV= PV=
PMT=
PMT= PMT=
FV=
FV= FV=
P/Y=
P/Y= P/Y=
C/Y=
C/Y= C/Y=
PMT: END BEGIN
PMT: END BEGIN PMT: END BEGIN

12. Nominal Rate of Interest - The stated rate of interest applied to your
investment.
6.5% per annum compounded semiannually
6.4% per annum compounded annually
6.45% per annum compounded monthly
Effective Rate of Interest - The interest rate if an annuity is
compounded annually.

13. HOMEWORK
Marge invested $2500 at 6.5% per annum
N=
compounded quarterly. Calculate the value
I%=
of her investment after three years.
PV=
PMT=
FV=
P/Y=
C/Y=
PMT: END BEGIN
Calculate the effective interest rate.
N=
I%=
PV=
PMT=
FV=
P/Y=
C/Y=
PMT: END BEGIN

14. HOMEWORK
Credit Card Interest
Calculate the effective interest rate of $1.00 invested at 18.5%
compounded daily for one year.
N= N=
I%= I%=
PV= PV=
PMT= PMT=
FV= FV=
P/Y= P/Y=
C/Y= C/Y=
PMT: END BEGIN PMT: END BEGIN

15. Shaina wishes to invest $2000 given by her grandfather. She has an
option of a guaranteed investment certificate earning 8.85%,
compounded quarterly, or a savings bond of 9%, compounded semi-
HOMEWORK
annually.
Which investment
N= N=
should she choose? I%= I%=
PV= PV=
PMT= PMT=
FV= FV=
P/Y= P/Y=
C/Y= C/Y=
PMT: END BEGIN PMT: END BEGIN
If each investment term is 5 years, what will be the difference in
their values at the end of the term?