Math Studies Review on Financial Math and Logic
1) Mary invests 500 AUD in a bank that offers a rate of 3.25% compounded annually.
a) Calculate how much money she has in the bank after 7 years.
b) Calculate the number of years it will take for the investment to triple.
2) Susan invests 1500 Euros for 5 years at a rate of 4.25% compounded annually.
a) Calculate the amount of money she has in total at the end of the 5 years.
b) The interest rate then drops to 3.75%. If she continues to leave her money in the bank find out how much it will be worth after a further 3 years.
3) Matt wants to invest 3000 USD in a savings account for college expenses.
a) Calculate the value of Matt’s investment based on a simple interest rate of 5% per annum, after 5 years.
Jackie tells Matt about a better account which offers interest at a rate of 4.5% per annum, compounding monthly.
b) Calculate Matt’s investment to the nearest USD after 5 years, if he follows Jackie’s advice.
4) Tyler wants to invest $1000 in a savings account for a car. The current interest rate is 4.75%. Calculate the value of Tyler’s investment after 3 years if it is compounded
a) yearly
b) twice a year
c) monthly
d) daily
5) Sam invests 6000 USD in a bank that offers interest compounded annually. His investment doubles in 15 years. Find the rate that the bank is offering.
6) Joey invested 10000 USD at the end of 1997. The interest rate was 5% per annum. How much interest would Joey have earned at the end of 2003 if
a) he had removed the interest from his account at the end of each year.
b) he had not removed the interest from his account at the end of each year.
7) Consider the statement “If today is Wednesday, then we are reviewing for the IB exam.” For this statement, write in words
a) the converse
b) the inverse
c) the contrapositive
8) Let the propositions be defined as:
p: Tom likes pizza
q: Ann likes liver
Write the following logic statements in words.
a) p q
b) p q
c) p q
d) p q
9) a) Complete the following truth table.
p / q / p / p q / p q / (p q) ( p q)T / T
T / F
F / T
F / F
b) Explain the significance of your results.
10) The propositions p and q are defined as follows:
p : Today is Wednesday and q : It is sunny
Write the following in symbolic form.
a) Today is Wednesday or it is not sunny but not both.
b) If today is sunny and it is Wednesday then it is not sunny.