Hi everyone.
Today, welcome to use a Texas BA II Plus Financial Calculator to solve a word problem
involving annuity.
Let's see an example, "Josephine purchased a car by making a down payment of $9,000 and
the monthly payments of $650 at the end of every month for three years.
If interest was 3.5% per year compounded monthly, what was the purchase price of the car?
And what is the total amount paid for interest?"
So the day Josephine purchase the car, she need to pay for the car price.
So she came up with $9,000.
That's the down payment.
Which is not enough to cover the car price.
That's why she also received a loan that requires monthly payments for three years.
So the sum of down payment and the loan is the car price.
Let's draw a timeline.
The day Josephine purchased the car, that's also the day she received the loan.
This loan amount is the present value.
Over the three year time period, Josephine's going to make monthly payments.
And at the end of the term she will pay it off.
So the future value of this loan will be zero.
To solve this problem, we need identify seven variables.
C/Y, compounding periods per year.
P/Y, payments per year.
And also on the calculator, this row, five buttons.
We need a N, I/Y, PV, PMT and FV.
So PV, we identify PV's our loan.
That's loan amount we're looking for.
And the future value will be zero.
And the PMT in this case is $650 every month because it's monthly payment, we know payments
per year is 12.
We also look at the interest, 3.5%.
We will drop the percent sign for calculator entry.
And we also know it's compounded monthly.
So C/Y is also 12.
12 compounding periods per year.
N is number of periodic payments.
So we'll follow the formula.
N is number of years times P/Y.
We know it's three year term and the P/Y is 12.
So N is 36.
Now we have all the variables we need to use calculator to find the value for PV.
Let's turn on by pushing on/off button.
Before we enter all these values let's make sure the calculator is set at the END mode
because the periodic payment happened at end of every month.
So go to second BGN.
You see my calculator is already at END mode.
If you need to change it, go second set, change to BGN, begin mode.
And second set again.
Now I'm back to end mode.
We can do second quit, exit.
Now for C/Y and P/Y, I go to second P/Y.
So enter P/Y, 12, enter.
Again, do not forget to push enter button.
Scroll down.
C/Y is also 12.
Great.
Let's exit by pushing second and quit.
Over here N is 36, so let's push 36 first and then N. I/Y is 3.5.
3.5 I/Y.
PV is unknown.
PMT is 650.
So when we look at all this three variables, be careful with the sign.
For Josephine, 650 monthly payment for her is money leaving her.
You can also consider as cash outflow.
So we should use negative for PMT.
Let's put a negative there.
Future value is zero.
Now let's compute present value.
So we have $22,182.73.
We round it 3 cents.
And this number come as positive.
As you can imagine, it's for Josephine to receive the loan, the cash inflow.
So it's positive.
So now we have the loan amount.
Let's calculate the car price.
It's down payment $9,000, plus the loan, 22,182.73.
So the answer would be 31,182.73.
That's the car price.
Now we have to answer a second question.
What is the total amount paid for interest?
Let's write it over here, interest paid.
For Josephine, in order to pay back this loan amount, she has to make monthly payments,
$650.
So we know $650 every month for three years.
That's total payment Josephine made.
To use this payments to cover the loan and that difference is the interest payment.
Let's do the calculation.
650 times 12, times three, subtract 22,182.73.
So it's $1,217.27.
And that is the interest paid for that loan.
Now we solve the problem.
Thank you for watching.