The Time Value of Money (2023 CFA® Level I Exam – Quantitative Methods – Module 1)
This is level one of the CFA program. The topic on quantitative methods and the reading on time value
of money. I'm guessing that you learned this way back in kindergarten. If you saved an amount today
and invested in a financial asset that had a positive rate of return then it's sometime in the future you
would have a larger amount. An investor with 100 today and this investor hopes to purchase an asset
one year from today now if that savings rate is ten percent the one hundred dollar savings that initial
savings will grow to 110 right that's an obvious answer. But what happens if those inputs are not quite
so obvious in other words suppose i changed that one hundred dollars today to fourteen thousand eight
hundred and sixty two dollars and the savings rate was four point three four six seven percent how
much would that grow to after uh after one year. If we earn 10 dollars worth of interest the first year
then we're going to earn ten dollars of interest in the second year so you might be tempted to say that
that future purchase amount is going to be 120 right ten and year one and ten in year two however
however however this ignores the value of compounding. The new shortwave math is much more
efficient than the old long way math.
When you turn it on you probably have two decimals so I want to show you how to change that quickly
so we're going to do a second format. Hit your second p slash y button that needs to be at one payment
per year, the default is 12. Set your payments per year so that we compound annually and we'll make
some slight adjustments to that as we go through. Time value of money problems are simple problems
problems that you should be able to get using the old math that I described to you earlier, but let's go
ahead and do this with our financial calculator. We'll say 5 is n over that time period and 7 is the interest
rate, and then we'll do that here in just a second. Bob saves 500 today, compute the value of the savings
in five years if the relevant interest rate is seven percent. When we're solving for the interest rate, we
need to be super sensitive about positivity and negativity so watch what I'm going to do here with your
calculators. Bill has 49 today and needs 92 in six years. This is super important here so let me go down
and clear this memory: when we did our very first calculation, we entered 100 and our answer was a
minus 110.
An annuity is a series of consecutive equal payments that begin one year from today. The interest rate is
the minimum rate of return an investor must receive in order to accept an investment, so we can view
that from your perspective too. Ten percent is the interest rate that is usually offered, but it doesn't
matter which direction they flow initially or at the end. An interest rate is also used and interpreted as
this term, a discount rate. This is a generic term that is used in time value of money. I want to break that
up into its component parts so notice that we have five of them here: real riskfree interest rate,
required rate of return, initial rate of return, final rate of return, and spread.
This is level one of the CFA program. The topic on quantitative methods and the reading on time value
of money. I'm guessing that you learned this way back in kindergarten. If you saved an amount today
and invested in a financial asset that had a positive rate of return then it's sometime in the future you
would have a larger amount. An investor with 100 today and this investor hopes to purchase an asset
one year from today now if that savings rate is ten percent the one hundred dollar savings that initial
savings will grow to 110 right that's an obvious answer. But what happens if those inputs are not quite
so obvious in other words suppose i changed that one hundred dollars today to fourteen thousand eight
hundred and sixty two dollars and the savings rate was four point three four six seven percent how
much would that grow to after uh after one year. If we earn 10 dollars worth of interest the first year
then we're going to earn ten dollars of interest in the second year so you might be tempted to say that
that future purchase amount is going to be 120 right ten and year one and ten in year two however
however however this ignores the value of compounding. The new shortwave math is much more
efficient than the old long way math.
When you turn it on you probably have two decimals so I want to show you how to change that quickly
so we're going to do a second format. Hit your second p slash y button that needs to be at one payment
per year, the default is 12. Set your payments per year so that we compound annually and we'll make
some slight adjustments to that as we go through. Time value of money problems are simple problems
problems that you should be able to get using the old math that I described to you earlier, but let's go
ahead and do this with our financial calculator. We'll say 5 is n over that time period and 7 is the interest
rate, and then we'll do that here in just a second. Bob saves 500 today, compute the value of the savings
in five years if the relevant interest rate is seven percent. When we're solving for the interest rate, we
need to be super sensitive about positivity and negativity so watch what I'm going to do here with your
calculators. Bill has 49 today and needs 92 in six years. This is super important here so let me go down
and clear this memory: when we did our very first calculation, we entered 100 and our answer was a
minus 110.
An annuity is a series of consecutive equal payments that begin one year from today. The interest rate is
the minimum rate of return an investor must receive in order to accept an investment, so we can view
that from your perspective too. Ten percent is the interest rate that is usually offered, but it doesn't
matter which direction they flow initially or at the end. An interest rate is also used and interpreted as
this term, a discount rate. This is a generic term that is used in time value of money. I want to break that
up into its component parts so notice that we have five of them here: real riskfree interest rate,
required rate of return, initial rate of return, final rate of return, and spread.
