Mathematics of finance
1- Prove which of the following options is the most interesting one:
a) To invest 5,000€ in a bank account that offers an annual simple interest rate of 6%, for 10 months
b) To invest 5,000€ in a bank account that offers an annual compound interest rate of 6%, for 10 months
The bank pays interests once per month
a)
b)
So, option b) is the best.

2- Prove which of the following options is the most interesting one:
a) To invest 5,000€ in a bank account that offers an annual simple interest rate of 6%, for 1 year
b) To invest 5,000€ in a bank account that offers an annual compound interest rate of 6%, for 1 year
The bank pays interests once per month
a)
b)
So, option b) is the best.

3- Prove which of the following options is the most interesting one:
a) To invest 5,000€ in a bank account that offers an annual simple interest rate of 6%, for 10 months
b) To invest 5,000€ in a bank account that offers an annual compound interest rate of 6%, for 10 months
The bank pays interests once per year
a)
b)
So, option a) is the best.

4- What do you prefer
a) To receive 1,000€ today?
b) To receive 1,030,3€ in 3 months?
c) To receive 1,062.8€ in 5 months?
The annual interest rate is 12%, and interests are paid once per month
Let’s find its value in 5 months:
a)
b)
c)

0

So, option c) is the best.

5- What do you prefer
a) To invest 5,000€ for 12 months, in a bank account that offers a simple interest rate of 10%
b) To invest 5,000€ for 12 months, in a bank account that offers a compound interest rate of 10%
In both cases, the bank will pay interests once per year.
a)
b)
So, both options are exactly the same.
6- Today I’ll invest 5,000€ in a bank account that offers a monthly interest rate of 1%. How much money will I have in that account in one year.
If we do it with simple interest rate:
If we do it