Exercises: Bank interest

After working over the summer as a camp counselor, you have managed to save $\$1500$. You decide to open a savings account that offers a simple interest rate of $2.5 \%$ per year. If you keep the money in the bank for exactly one year without making any transactions:

1. a) What interest ($I$) will your capital generate at the end of the year?
2. b) What will be the final capital ($C_f$) available in your account?

To buy a state-of-the-art tablet costing $\$600$, you take out a small loan from a financial institution that charges a simple interest rate of $6 \%$ per year. If you agree to repay the money together with the interest in a single payment after 8 months, calculate:

1. a) The rate ($r$) expressed as a decimal.
2. b) The time ($t$) expressed in years.
3. c) The total interest you will have to pay for the loan.

Your grandparents have given you $\$2000$ for your 16th birthday and you decide to invest it in a bank product at compound interest of $3 \%$ per year for 3 years. Since it is compound interest, the interest is compounded annually (added to the capital to generate new interest).

Calculate the final capital ($C_f$) you will have after 3 years using the formula:

$$C_f = C_0 \times (1 + r)^t$$

Look at the following bank advertisement aimed at young savers:

"Grow your savings! Deposit $\$3000$ with us and after two years we will give you back $\$3180$."

Assuming that the bank applies annual simple interest, identify the following financial elements:

1. Initial capital ($C_0$).

2. Time of the transaction ($t$).

3. Total interest generated ($I$).

4. Annual interest rate ($R$) as a percentage.

Calculate what initial capital ($C_0$) we should deposit in a bank account so that, at a simple interest rate of $4 \%$ per year, we obtain exactly $\$120$ in interest after one year.

An online microloan platform offers fast loans at a monthly simple interest rate of $1 \%$. If a user requests $\$400$ to repair their motorcycle and plans to repay everything at the end of a quarter (3 months):

1. a) What is the interest they will pay each month?
2. b) What is the total amount (principal + interest) they will repay at the end of the three months?

A bank offers two types of accounts for young people:

• Account A: Simple interest of $3.1 \%$ per year.

• Account B: Compound interest of $3 \%$ per year.

If you are going to deposit $\$1000$ for just one year, which of the two accounts will give you a greater profit at the end of that year? Justify your answer by showing the necessary calculations.

Graph the growth of the accumulated interest of a $\$1000$ investment at a simple interest rate of $5 \%$ per year over the first 4 years.

First complete the data table (accumulated interest at the end of each year) before drawing the graph:

• Year 1: $I = \dots$

• Year 2: $I = \dots$

• Year 3: $I = \dots$

• Year 4: $I = \dots$

Then, draw a set of axes: time (in years, from 0 to 4) on the horizontal axis and interest (in dollars) on the vertical axis. Choose a suitable scale, mark the points from the table (plus the point for year 0) and connect them.

You can do it on paper and send a photo with your answer.

Mateo has received a prize of $6\,000$ dollars and decides to invest it for 4 years. His bank offers him two different options to earn a return on his money:

• Option A: A simple interest deposit with an annual rate of $4.5$ %.

• Option B: A compound interest savings account with an annual rate of $4.2$ % and annual compounding of interest.

Calculate the final amount he would obtain with each option and explain which one is more financially advantageous for him at the end of the 4 years.