In this section we will apply what we've learned about exponential functions to understand banking and loans. As an introduction, we will look at how the amount of money owed on a loan grows exponentially:
You can see the .pdf version of the lecture here.
Because compound interest (interest earned on previous interest) increases the amount of the loan, banks have an incentive to compound more frequently than once per year! Let's explore what happens to our loan as the number of times per year that the interest is compounded changes!
You can see the .pdf version of the lecture here.
Using what we learned in our first example, we will find a formula for the amount of money owed on a loan in a more general form:
You can see the .pdf version of the lecture here.
Since the amount on the loan increases as the number of times per year that the interest compounds increases, why not compound more and more? Let's explore what happens as interest is comounded more and MORE frequently.
You can see the .pdf version of the lecture here.
Here we will recap the formulas that we have found for the amount of money owed on a loan.
You can see the .pdf version of the lecture here.
If we put money in the bank then we are giving the bank a loan, which will earn us interest. We will now look at an example looking at how our money can grow in the bank. In particular, we want to know how much money we would need to put away today to have $3000 in the bank in 5 years if we are earning 2% interest compounded monthly.
You can try it on your own here, either before or after watching the lecture figuring it out.
You can see the .pdf version of the lecture here.
In the next example, we will assume that we have $1000 to put in the bank earning 4% interest comounded continuously and will find out how much money we have after 5 years.
You can try it on your own here, either before or after watching the lecture figuring it out.
You can see the .pdf version of the lecture here.
Continuing our last example where we have $1000 to put in the bank earning 4% interest comounded continuously; how long will it take before we double our money to $2000?