Welcome to this Time Value of Money calculations
tutorial using the BA II Plus calculator, compiled by Andrew Rossman.
In this tutorial we will only be using these ”Time Value of Money” keys.
That is, we will not be changing P/Y and C/Y values. P/Y and C/Y will be left at their
default values 1. So if you plan on changing them, please see
other videos posted on this channel. We will enter incoming payments as positive
and outgoing payments as negative. You can change the decimals to your desired
number of decimal places by pressing 2nd FORMAT. You can choose 9 to display all decimals but
I will leave it at 2. Press enter, and then 2nd quit.
Before solving any problem, Press 2nd CLR TVM to clear these TVM entries
You can always check the value stored in the TVM entries by pressing the Recall button
and then the TVM key. For example, RCL PV shows 0, and RCL PMT also shows 0 because
I cleared the TVM entries. So let’s look at the first example:
Solving for Payment. Laura takes a 15-year, $500 000 mortgage, on a new condo. At an interest
rate of 4% (that is compounded monthly), what is the monthly payment?
So we begin by pressing 2nd CLR TVM to clear previously done work.
Since we have monthly payments for 15 years, there will be 15x 12 payments which equals
180 payments in total. So we input 180 N
For the interest rate, we divide the 4% by 12 by pressing 4 divided by 12 equals 0.33
and then press I/Y. Note that there are more decimal places not
displayed by the calculator because it is set to 2 decimal places. Although the remaining
decimals are not displayed, they will still be used in the computations.
Note that it will be incorrect to just type 0.33 and press I/Y. You will be missing the
remaining decimal places not displayed by the calculator.
For Present value we enter 500,000 Present Value
Since we will have 0 balance at the end of 15 years, we enter 0 Future Value
And then CPT Payment. And that gives $3,698.44
Note that the value is negative because we input the present value as positive.
The next example shows how to solve for Present Value.
Helene is planning ahead for her daughter Paula’s college tuition. Paula begins college
in 5 years and will need $80,000. How much would Helene have to invest today at 6% compounded
annually to have $80,000 in 5 years? This is a compound interest problem where
the present value is required. We begin by clearing TVM entries by pressing
2nd CLR TVM. Since the duration is 5 years and interest
is compounded annually, we input 5 for N by pressing 5 N.
For 6% interest rate, we press 6 I/Y Since there are no recurring payments we input
0 PMT. For the future value, we enter 80,000 FV.
And then compute PV Which gives 59,780.65. Next let’s solve for future value.
Josh has an investment account with $50,000. If Josh earns 6% per year and contributes
$400 each month, how much will his investments be worth in 10 years?
Note here that interest is compounded per year. Therefore, interest will not be applied
to the $400 monthly payments until after 1 year. That is, until the payments add up to
12 x 400 which is $4800. In essence, we actually have 10 conversion
periods over the 10 years. So we input 10 N
For interest rate we input 6 I/Y We input 50,000 PV
And 4800 PMT. We then compute future value which gives 152,810.20
Next we solve for time. Example 4 – Solving for Time
Steven has $25,000 in credit card debt. His credit card charges 2% in monthly interest
and Steven pays $1,000 each month toward the balance. If Steven doesn’t make any further
purchases, how many months will it take to fully repay his debt.
At 2% monthly interest rate, let’s input 2 I/Y.
25,000 PV for the debt amount Since the payment is made to reduce the debt,
we input it as a negative value: 1,000 negative, and then PMT
Since the debt will be fully repaid, we input 0 for the future value: 0 FV.
And then compute N which gives 35 months. Next we solve for interest rate Martin’s savings account has $25,000 today.
In 5 years, the account is worth $32,000. What is the annual interest rate?
Since interest is compounded annually for 5 years, we input 5 N.
We’ll have to input the 25000 present value as negative because it is an outflow. So we
enter 25 000, negative, PV. We enter 0 PMT as there are no periodic payments.
For future value we enter 3200 FV And then compute interest rate I/Y which gives
5.06%. And that concludes this tutorial.
Thanks for watching.