ib math studies year 1 7-6 intro to compound interest...2019/03/07 · when you are borrowing...
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Name_________________________________ Date_______________
IB Math Studies Year 1 7-6 Intro to Compound Interest
Learning Goal:
What is compound interest? How do we compute the interest on an investment?
Warm-Up: Let’s say that you deposit $100 into your savings account today. This bank account gains 2% interest
every year. If you don’t withdraw any money
a. How much money would you have at the end of the first year?
b. How much money would you have at the end of the second year?
c. In these two years, how much interest (money) did you gain?
d. Is the money in the savings account increasing by the same about each year?
Interest is the percent of money charged to money borrowed or percent of money earned on an
investment.
When you put money into a savings account, the bank often pays you interest. That
interest is the incentive for you to keep the money in the bank, your account is gaining this
interest.
When you are saving money …
When you take out a loan (or borrow money) to pay for something like a house or car you have to pay interest on that money.
When you are borrowing money…
Compound Interest
When you borrow money or deposit money interest accumulates per year (also called per annum)
. This means that the interest gained each year is based off the current amount of money in the
account, not the original amount deposited.
Compound Interest with the Calculator All graphing calculators have an in-built finance program that can be used to investigate financial
scenarios. This is called a TVM Solver, where TVM stands for the “time value of money”. The TVM
Solver can be used to find any variable if all the other variables are given. TVM solver is found under the
APPS button on the calculator. Press APPS
For the TI-83/84, the abbreviations used are:
N = total number of times the account is compounded
(the number of compounding periods per year × the number of years)
I% = annual interest rate (kept as a percent)
PV = principal (present value)
PMT = monthly payment (always 0 for this class)
FV = future value
P/Y and C/Y = number of compounding periods per year
In this course, you will be responsible for the following compound interest periods. Compound interest is
the number of times you will earn interest on your investement per year (per annum).
Annually Semi (Half)-Annually Quarterly Monthly
A Couple of Notes
In this class, you will only be solving for variables I%, PV, FV, and N.
In order to show your work, you must make a key for all your substitutions in the calculator.
I% is always entered as a percent, not a decimal.
PV is always entered as a negative number.
P/Y and C/Y will always be 1, 2, 4, or 12.
To get an answer, enter the variables that you know on the appropriate lines and then scroll to the
line for the variable you wish to solve for and press Alpha Enter
MODEL PROBLEM: Holly invests 15000 GBP in an account that pays 4.25% per annum compounded
monthly. How many GBP will be in her account after 5 years?
Solving for Future Value – FV
Remember to enter the present value as a negative number!
WE TRY: John deposits $4000 into a bank
account. The bank’s stated rate of interest is 6%
per annum compounded quarterly. Calculate the
value of John’s account after 8 years.
YOU TRY: Morimi invested 700 JPY at 6.3%
interest compounded quarterly for 15 years.
How much money did Morimi have at the end of
the 15th year?
Solving for Present Value – PV
The calculator will give you the present value as a negative number. Write it as a positive #!
WE TRY: Mr. Gino invested x dollars in an
account that pays a nominal annual interest rate of
3.6% compounded sem-annually in order to buy a
speedboat. After 18 years, he will have $35,300
in the account. Calculate the value of x.
YOU TRY: Carmen deposited Argentine pesos,
ARS, in a bank account which pays a nominal
interest rate of 17%, compounded yearly. After
three years, the total amount in Carmen’s account
is 10,000 ARS. Find the amount that Carmen
deposited in the bank account.
Solving for Interest Rate
Remember to enter the present value as a negative number!
WE TRY: Jacob invested 10000 EUR for
30 years. The investment has a nominal
annual interest rate 𝒓% and is compounded
annually. After 30 years, the investment
will be worth 35300 EUR.
Calculate the value of 𝒓 to the nearest
percent.
YOU TRY: At what interest rate, compounded
annually, would you need to invest $100 in order
to have $125 in 2 years?
Practice
1. Samantha puts €15000 in a bank account earning 6% annual interest compounded monthly. How much total money will she have after 20 years?
2. Michael wants to make an
investment and accumulate
25,000 EUR over a period of 18
years. He finds an investment
option that earns a nominal
interest rate of 8% compounded
quarterly. Find the amount of
money that Michael will have to
invest to have 25,000 EUR at the
end of 15 years.
3. You are planning to send
your daughter to college in 18
years. You determine that in the
end you will need $100,000 in
order to pay for tuition, room
and board, etc. At what interest
rate, compounded annually,
would you need to invest
$20,000 in order to reach your
goal in 18 years?
Name_________________________________ Date_____________________
Lesson 7-6 Homework
1. Carla has 7000 dollars to invest in a fixed deposit which is compounded annually. She aims to have
14000 dollars after 10 years.
Calculate the annual interest rate needed for Carla to achieve her aim.
2. Diogo deposited 8000 Argentine pesos, ARS, in a bank account which pays a nominal annual interest
rate of 15%, compounded monthly.
Find how much Diogo has in his account after 2 years.
3. Jacob invested 𝒙 EUR for 43 years. The investment has a nominal annual interest rate of 3.2% and is
compounded quarterly. After 43 years, the investment will be worth 52300 EUR.
Calculate the value of Jacob’s initial investment, 𝒙. Give your answer to two decimal places.
4. Daniela is going for a holiday to South America. She flies from the US to Argentina stopping in Peru
on the way. In Peru she exchanges 85 United States dollars (USD) for Peruvian nuevo sol (PEN). The
exchange rate is 1 USD = 3.25 PEN and a flat fee of 5 USD commission is charged.
(a) Calculate the amount of PEN she receives.
At the end of Daniela’s holiday she has 370 Argentinean peso (ARS). She converts this back to USD at a
bank that charges a 4% commission on the exchange. The exchange rate is 1 USD = 9.60 ARS.
(b) Calculate the number of ARS that Daniela must pay in commission.
(c) Calculate the amount of USD she receives.