Cenk Yildiran

Writing about lots of unrelated topics…

April 24, 2023

The Future Value of Money With Different Compounding Periods

In this post, I will show you the importance of the compounding period in calculating the future value of money.

Image by Nattanan Kanchanaprat from Pixabay

The setup for this example is as follows: You have $10,000 deposited in a saving account with a fixed annual interest of 5% for ten years.

The Future Value of Money with Different Compounding Periods

Let’s quickly calculate what happens to your money at the end of ten years with annual compounding:

$PV = \$10,000$
$N = 10 \; years$
$r = 0.05 (5\%)$
$FV = ?$
$FV = PV (1 + r)^N$
$FV = \$10,000 (1 + 0.05)^{10}$
$FV = \$10,000 (1+ 0.05)^{10}$
$FV = \$10,000 (1.05)^{10}$
$FV = \$10,000 \times 1.6289$
$FV = \$16,288.95$

Your $10,000 becomes $16,288.95 in 10 years with a 5% fixed annual interest rate compounded annually.

Now let’s look at what happens if the money is compounded in different frequencies. To do that, we need to introduce a modified formula:

$r = annual \; interest \; rate$
$N = number \; of \; years$
$m = compounding \; periods \; (per \; year)$
$PV = Present \; Value$
$FV = Future \; Value$
$FV = PV(1 + \frac{r}{m})^{m \times N}$

Monthly Compounding

$N = 10 \; years$
$r = 0.05 (5\%)$
$m = 12 \; months$
$PV = \$10,000$
$FV = ?$
$FV = PV(1 + \frac{r}{m})^{m \times N}$
$FV = \$10,000 (1 + \frac{0.05}{12} )^{12 \times 10}$
$FV = \$10,000 (1 + 0.00416 )^{120}$
$FV = \$10,000 (1.00416 )^{120}$
$FV = \$10,000 \times 1.6457$
$FV = \$16,456.98$

Your $10,000 becomes $16,456.98 in 10 years with a 5% fixed annual interest rate compounded monthly. This (monthly compounding) is larger than the previous case (yearly compounding) by $168.03.

Weekly Compounding

$N = 10 \; years$
$r = 0.05 (5\%)$
$m = 52 \; weeks$
$PV = \$10,000$
$FV = ?$
$FV = PV(1 + \frac{r}{m})^{m \times N}$
$FV = \$10,000 (1 + \frac{0.05}{52} )^{52 \times 10}$
$FV = \$10,000 (1 + 0.000962 )^{520}$
$FV = \$10,000 (1.000962 )^{520}$
$FV = \$10,000 \times 1.6487$
$FV = \$16,487.20$

Your $10,000 becomes $16,487.20 in 10 years with a 5% fixed annual interest rate compounded weekly. This (weekly compounding) is larger than the yearly compounding by $198.25 and larger than the monthly compounding by $30.22.

Official Curriculum for CFA Level I: https://amzn.to/414Ev3r

An easy-to-read book for personal finance: https://amzn.to/3AP5aH2

Make a one-time donation

Make a monthly donation

Make a yearly donation

Choose an amount

¤5.00

¤15.00

¤100.00

¤5.00

¤15.00

¤100.00

¤5.00

¤15.00

¤100.00

Or enter a custom amount

Your contribution is appreciated.

Donate Donate monthly Donate yearly

CFA

Finance, interest, investing, investment, money

Posted by:

cenk-yildiran

About Me

My name is Cenk, and I am an economist. I write on this internet site on economics, econometrics, finance, value-investing, programming, calculus, basketball, history, foods, books, self-improvement, well-being and productivity. This internet site is a personal blog, and the posts reflect my personal views and do not represent where I have been working.
For my academic works, please visit this site: https://cenkufukyildiran.academia.edu/
Posts related to financial markets, trading, investing and similar posts are not for financial advice purposes.

Cenk Yildiran