Mastering Time Value of Money A Practical Guide to Financial Calculator Utilization
I’m gonna show you how to use financial calculator for the questions
of time value of money.
financial calculator
Before we start working on the questions, you will need to download the financial calculator
from the App Store.
Just search “financial calculator”, you will find it.
After downloading it, just open it.
That’s what you will see.
We will use TVM Calculator for the calculation of time value of money.
Inside TVM Calculator, you may key in the figures in the empty space.
If you want to get the answer, just press on the button.
You can also change the compounding period here.
Future Value of a Single Amount
First part, let’s calculate the future value of a single amount.
Jane places $800 in a savings account, paying 6% interest compounded annually.
She wants to know how much money will be in the account at the end of five years.
Let’s analyze this question.
$800 is the money that Jane is going to save, which means she is going to pay now.
So, this is PV, and it would be negative 800.
Paying money would be negative, receiving money would be positive.
6%, this is the annual interest rate, I/Y.
5 years, this is the period, N.
To get the answer, you need to calculate the future value, FV.
Now, turn to the financial calculator, set annually compounding, and set end mode.
Then key in, negative 800 for PV, the present value.
Key in 6 for I/Y, the annual rate.
Key in 5 for N, the period.
Lastly, press FV, then you will get the answer.
This amount of money will be in the account of Jane at the end of five years.
Present Value of a Single Amount
Next, let’s calculate the present value of a single amount.
Mary wishes to find the present value of $1,700 that will be received 8 years from now.
Mary’s opportunity cost is 8%.
This question means, after 8 years, Mary will receive $1,700.
That means, $1,700 is FV.
What you need to calculate is PV.
Using financial calculator, set annually compounding, and set end mode.
Then key in, FV = 1,700, N = 8, I/Y = 8, last step press PV.
You will get the answer.
Negative PV means, this is the money that you will have to pay now.
Annuities
We have just discussed the first pattern of cash flow which is single amount.
Now let’s look at the second pattern, annuities.
Annuity is a series of equally-spaced cash flows, occurring over a specified number of
period.
That means, same amount of cash flows will be repeating.
Annuities can be either inflows or outflows.
There are two types of annuities.
The first type is ordinary annuity.
An ordinary annuity has cash flows that occur at the end of each period.
The key word is, the end of each period.
The second type, annuity due.
An annuity due has cash flows that occur at the beginning of each period.
The key word is, the beginning of each period.
An annuity due will always be greater than an equivalent ordinary annuity, because interest
will be compounded for an additional period.
Examples of Annuities
Let’s take an example.
If you buy a bond, you will receive equal semiannual coupon interest payments over the
life of the bond.
Equal semiannual coupon interest payments are annuity.
Another example, if you borrow money to buy a house or a car, you will have to pay a stream
of equal payments.
Loan payments are annuity as well.
Types of Annuities
Tracy is choosing which of the two annuities to receive.
Both are 5-year $1,000 annuities; annuity A is an ordinary annuity, and annuity B is
an annuity due.
Tracy has listed the cash flows for both annuities as shown here.
For Annuity A, the ordinary annuity, it means Tracy will receive $1,000 at the end of each
year.
But for Annuity B, the annuity due, it means Tracy will receive $1,000 at the beginning
of each year.
To show this is the cash flow received at beginning of Year 1, we will write the cash
flow at Year 0, which is one year forward.
Similarly, cash flow for beginning of Year 2, we will write it at Year 1.
Note that, the amount of both annuities is $5,000.
But, in fact, they have different values.
Let’s put it into calculation.
Future Value of an Ordinary Annuity
Tracy wishes to determine how much money she will have at the end of 5 years, if she chooses
annuity A, the ordinary annuity, and it earns 7% annually.
Using financial calculator, set annually compounding, and set end mode.
Then key in, PMT = negative 1,000, N = 5, I/Y = 7.
Last step press FV, you will get the answer.
Positive FV means, this is the money that you will receive after 5 years.
Future Value of an Annuity Due
If we slightly modify the question,
Tracy now wishes to calculate the future value of an annuity due for annuity B. Recall that,
annuity B is a 5-year annuity with the first annuity beginning immediately.
Using financial calculator, set annually compounding, and set beginning mode.
