Compound interest~ SAVE YOUR MONEY!
There are lots of options for saving your money. Banks make more money using yours as leverage (they invest your money)… the more money they have, the more money they can make!
Banks offer you incentives for leaving your money in their care. They offer accounts that pay you INTEREST- they grow your money by a certain percentage (rate) each month.
Some accounts that grow your money:
· RRSP’s
· Mutual Funds
· High interest savings accounts
· GIC’s
ALL of these accounts help you to earn money just by sitting in the bank- but they each work in a different way. Some of these accounts are guaranteed, and some are risky… some grow your money fast, and some are slow.
ESSENTIALLY, these accounts all work on the principal of COMPOUND INTEREST.
COMPOUND INTEREST:______
Here is how it works:
Dollar Amount in savings account / Interest / YEAR / New Balance ($) at end of year4% / 1
4% / 2
4% / 3
The more money you have, the faster your money grows!
Compound Interest grows when a % gain or loss occurs repeatedly, and the value to which interest is applied changes over time. The more you have, the more you make!
The magic formula:
A=P(1 + r)
A=
P=
r =
n =
Example: Imagine that you have invested $1000 over 3 years, at an interest rate of 10% annually. How much money will you have after three years?
Fill the known values into this formula:
A=P(1 + r)
A=
P=
r=
n=
TRY:
Money coming in…
1. Jenille invests $2000 at the bank for 6 years at an interest rate of 3% per year. How much does she have after two years?
A=P(1 + r)
2. Diana has a tuition savings of $4,500 locked into a high interest savings account for 4 years. She gets an annual interest rate of 4%. How much money does she have after 4 years?
A=P(1 + r)
TRY:
Money going out…
3. Iqbal is ready to buy a big-screen TV. He puts $1,200 cost of the TV on a “Best Buy” credit card and lets it sit there for one year. The annual interest rate on the card is 23.5% How much money will he owe by the end of the year?
A=P(1 + r)
4. Chaud lends money to his best friend, from his emergency fund. He lends $10,000 to his friend for 3 years, at a low interest rate of 2% per year. How much money did Chaud’s friend pay back to him by the end of the three years?
A=P(1 + r)
Finding the Principal: Find out how much money you started with….
HINT: Isolate the unknown variable.
Given: A=P(1 + r)
1. Your current GIC account balance is $5,800.00 You have had your money in this account for 4 years, at a steady interest rate of 5%. How much money did you start with?
2. You have not been very good at paying your credit cards lately- whoops! Your current credit card bill is $2,644.00 and the charge has been growing steadily for the past 1.5 years. Sadly, you have a HIGH interest rate of 24%. How much money did you owe initially, 1.5 years ago?
New challenge: when compound interest isn’t so simple…
Up until now we have been solving questions with ANNUAL compounding periods (annual interest).
Sometimes banks offer you interest that compounds SEMI-ANNUALLY, QUARTERLY, or MONTHLY.
There is another variable thrown into the mix… t
“t” is the number of times interest is compounded per year.
This will change 2 of your values: your r: and your n:
P = principal
r = annual interest rate
t = number of times the interest is compounded per year
n = number of years
When your interest rates compound faster or slower than annually, you need to use this formula.
Fill in the chart:
______means ______times per year.
Compound period / ”t” valueDAILY
WEEKLY
BIWEEKLY
MONTHLY
BIMONTHLY
QUARTERLY
SEMI-Annually
Annually
USE the formula below to complete the table. Watch the Compound Period carefully!
Principal (P) / Interest rate (r),decimal / Compound Period (t) / Years (n) / A
2500 / 0.075 / semi-annually
= / 5
700 / 0.04 / Quarterly
= / 2
18 000 / 0.05 / Monthly
= / 7
TRY:
1. Kim invests $1850 at 8% interest compounded quarterly for 9 years. How much will her investment be after 9 years?
2. You need $25 000 for you university tuition in 5 years. How much will you need to invest today at 7.5% interest compounded monthly?
3. Gary and Larry do not get along very well…Larry decides to lend Gary some money in hopes of making some money himself.
Now, Gary owes $6000 to his big brother Larry. Larry has decided to charge him an interest rate of 4% compounded bimonthly. Gary will pay Larry off in full (the full amount), in 2 years. How much will Gary pay Larry in 2 years?
4. You want to retire with $500 000. You have two options to save:
a) You can invest in a GIC at 10% compounded quarterly for 21 years.
b) You can invest in a GIC at 7% compounded monthly for 30 years.
Which option will you choose?