Hi, everyone.
Today, we're going to use a Texas BA II Plus financial calculator to solve an annuity problem.
Let's see the example.
Alex has decided to start saving up for vacation in two years.
He already has $500 saved today.
For the first year he plans on making end-of-month contribution of $100, and then switching to
end-of-quarter contribution of $250 in the second year.
If the account earns 4% compounded monthly, how much money will Alex has saved in two
years?
So first let's draw a timeline.
We're looking at two year time period.
So beginning, that's right now, Alex already have $500 saved up, and for the first year
he will make end-of-month contributions of $100 every month.
So for the first year he will make PMT of $100, so that's every month for 12 months.
And end of the year he will switch to end-of-quarter contribution of $250, that's for second year,
end-of-quarter payment.
He'll make periodic payment of $250 for the second year, and how much money will Alex
has saved in two years?
Our question is, how much money will he have at the end of the two years?
Because the periodic payment had made change for year one and year two, we have to look
at this problem in two parts.
First part, with the present value of $500 and the PMT of $100 monthly for the first
year, we'll need to calculate a future value.
And this future value will become the present value when we look at the second year.
The present value together with PMT of $250 we will calculate a future value and that
is what we're looking for, how much Alex will have saved in two years.
Let's look at this question in two steps.
Step one, we're looking at the first year.
In order to use financial calculator, we have to identify the following seven variables.
And, also because we're looking at an annuity problem, we know all the periodic payments
happen at the end of the month.
Let's write it here, our setting will be end.
For all the variables, we already know PV is $500, and the periodic payment is $100.
Considering this money as investment, so when Alex put this money into the bank, the money
leaving him, when you use calculator, you may enter them as negative.
Interest rate is 4% compounded monthly, so 4% compounding monthly.
That means compounding period is every month, 12 compounding every year.
And the PMT is also a monthly payment, so 12 times payment every year.
N is number of years times PY, which give us number of periodic payments.
In this case it's one year times 12 is 12.
And with all those six variables, we will be able to compute future value.
And now again, keep in mind that future value we're turning into the present value for the
second step.
Let's write out the second step.
Again, we will be working with a END mode because the payment is end-of-quarter.
CY, PY, N, IY, PV, PMT and the future value.
Remember this future value will become our new present value, so we will have that answer.
Interest rate is four, compounding is still 12, periodic payment is end-of-quarter payment,
so it's four times each year, and payment amount is $250.
N is number of years times PY.
We're looking on the second year, so that is one year.
One year times PY, which is four, so N is four.
And after we identify this PV from step one, we can just compute future value.
Okay.
Now we're ready to use the financial calculator to solve the problem.
First, turn on the computer by pushing on and off button.
Let's make sure the calculator is in the right mode, which is END.
If yours is not, you can go to a second BGN to change it.
You just push second, enter, and then once you're done, you do second and quit.
Make sure you're in END mode.
Now to put in CY and the PY number, go to second, PY, so PY is 12, enter, scroll down.
CY is also 12 by default, second and quit.
Now for these five values, we need enter four of them and then we can compute the last one.
So 12 is for N and the interest rate IY is four.
So four, IY.
PV is 500, so 500 let's make it negative PV.
PMT is 100, again we'll make it negative.
Compute future value you'll be 1742.617059.
This future value calculated to be 1742.617059.
Notice, I did not round it here because it's a middle step.
We'll only round it once we calculate our final results.
Now step two, we'll enter all the information and calculate again.
This stays END mode, I don't need to change it.
CY is 12, so second, PY is four, enter, scroll down.
CY is 12, enter and then second, quit.
Get out.
Now, for N is four.
So four for N, interest rate the same.
And the PV is this new value, 1742.617059.
Now, you may change the number to negative because you can consider that money as, again
you invest money into bank.
And if you do use negative, make sure your PMT also entered as negative because again,
that's your constant end-of-quarter contribution.
Let's make PV negative and the PMT also negative.
250 negative PMT, and let's compute for future value.
It's 2828.76.
Notice now, I round it to two decimals, because we're talking about money, so it only makes
sense to be accurate up to cents.
Now, we'll have solved the problem.
At the end of the two years, Alex will have saved $2,828 and 76 cents.
Thank you for watching.