More Time Value of Money Tutorials
|
In essence, time value of money refers to the growth
of 1 dollar as time increases. 1 dollar today is worth
more 10 years down the road because it can earn interest
payments. How much is 1$ worth 10 years down the road?
This answer depends on various factors such as the interest
rate, monthly/quarterly/annual compounding, payment contributions
or withdrawals and more.
Here is some basic terminology of the
time value of money function:
Future Value - Refers
to how much an investment grows over a certain period of
time. Example $5000 invested today grows to over $29,010
in 5 years of time with an interest rate of 5% compounded
annually.
Present Value - Refers
to how much an investment is worth today. Therefore from
the example above, if i invest $5000 today, the Present
Value (PV) is $5000. The future value in 5 years is $29,010.
Compounding Interest - This
is the process of accumulating interest earnings in an investment
over time, to further increase the interest earnings. Here's
a simple example:
- You invest $100 today into a savings
account earning you 10% interest rate compounded annually.
- At the end of Year 1, you'd have
$100 + ($100 * 10%) = $100 + $10 = $110
- At the beginning of Year 2, the total
you have accumulated thus far is $110.
- At the end of Year 2, you'd have
$110 + ($110 * 10%) = $110 + $11 = $121
- At the beginning of Year 3, the total
you would have accumulated thus far is $121.
- At the end of Year 3, you'd have
$121 + ($121 * 10%) = $121 + $12.1 = $133.1
In a matter of 3 years, you were able
to grow $100 to $133.1 with 10% interest compounded annually.
This is the power of compound interest !! Imagine if you
had initially invested $100,000 into the same account. In
3 years, the total amount it would grow to is $133,100.
Therefore, you earned $33,100 in 3 years thanks to compound
interest!!
Formula for Future Value
The formula for future value is Future
Value = $1 x (1 + r)t where r stands for the
interest rate, and t stands for the # of years.
To confirm the above answers we got
for the $100 invested today, we have:
2 years= $100 x (1+0.1)2
= $121
3 years= $100 x (1+0.1)3 = $133.10
4 years= $100 x (1+0.1)4 = $146.41
5 years=$100 x (1+0.1)5 = $161.05
Here's a table below to summarize these
calculations:
| Year |
Beginning Amount |
Simple Interest |
Interest on Interest |
Total Interest Earned |
Total Ending Amount |
| 1 |
$100 |
$10 |
$0 |
$10 |
$110 |
| 2 |
$110 |
$10 |
$1 |
$11 |
$121 |
| 3 |
$121 |
$10 |
$2.1 |
$12.10 |
$133.10 |
| 4 |
$133.10 |
$10 |
$3.31 |
$13.31 |
$146.41 |
| 5 |
$146.41 |
$10 |
$4.64 |
$14.64 |
$161.05 |
Graphical Representation of Compound
Interest
Notice the column "Simple Interest."
Simple Interest is simply $100 x 0.1 = $10. Since simple
interest is NOT compounded, you will always earn a flat
rate of $10 generated by the 10%
Homework
Question: If you have $200 to invest now,
how much will it be worth in 5 years with an interest rate
of 5% compounded annually?
Answer:
$200 x (1+0.05)5 = $255.25
|
