1. Title Slide
Let's start this chapter by just putting aside the simple interest approach
for now, as apart from a few exceptions, it's not found very often
in finance. Instead, let's focus on compound interest.
In chapter one, when we calculated the future or present values using compounding
interest, we only considered annual compounding or discounting periods.
Let's see what happens when interest is earned or compounded more frequently.
Let's start with a nominal interest rate of 10%. Think about the nominal
interest rate as the annual interest rate before the effect of any compounding.
Let's also start with a present value today of $1000.
When we looked at compounding interest back in chapter one, we assumed that
interest compounded annually. This means if you invested $1000 today with
a nominal rate of 10%, you'd have 1000 multiplied by one plus 10%,
which is 1100 at the end of the year.
However, the nominal rate could be compounded semi annually.
This means you're earning 10% divided by two, which is 5%
every six months. In the first six months, this would give you 1050. In
the second six month, you'll earn another 5%, but this time on 1050,
meaning at the end of the year, you'll have 1102.5. What's really crucial
is that you'll end up with slightly more than you did with annual compounding.
Well, what about quarterly compounding? Each quarter, you'll earn 10% divided
by 4 which of course is 2.5%. Meaning after three months you'll have
1025, after six months, you'll have 1050.63, after nine months, you'll have
1076.89 and at the end of the year, you'll have 1103.81. Again,
what's crucial here is that using quarterly compounding, you'll end up with
a higher future value after 12 months than both under annual compounding
and semi annual compounding.
2. Let's practice!