Present Value and Future Value

leea9999_kl1lc96m Finance

The fundamental building blocks of Finance include the concept of the present and future value. What is future value? I think most students have learned it in their secondary school. When you put money into a bank, you will receive interest on your deposit (as far as I know, the interest rate in Hong Kong is virtually 0; nevertheless, I need to make my point). Here is the formula:

I think that you should have heard about the power of compounding. If you want to be rich, you should better know this concept well (Warren Buffett is a big fan of the power of compounding). For example, if you have $100 deposit into a bank that pays 5% interest, you will get $162.89 after 10 years. You will get $62.89 in total after 10 years without working for your income (this is what people call passive income, but assuming that the bank does not go bankrupt after 10 years). Is it fascinating?Here are the cash flows over 10 years:

In year 1, you will receive $5 of interest. In year 2, you will receive $5.25 of interest and so on. Notice that the amount interest you get keep increasing over the year. The is the power of compounding. It is like a snowball that grow over time on the way to a destination in the future.


Okay, let’s add some complexities into the equation. How about putting $100 into a bank that pays 5% every year for 10 year? You can calculate the amount by following formula:

Therefore, using the above formula, you will get $1257.79 after 10 years if you deposit $100 every year for 10 years into the bank that pays 5% interest. Over that period of time, you will obtain a total interest of $257.79 without working for your income.

Of course, I can add more complexity into the equation. For example, if you think that you are going to have a raise of 10% every year, so that your deposit will grow 10% every year. you can calculate the amount by following formula:

This is what people call growing annuity. If your deposit, which is growing at 10% rate, was put into a bank that pays 5% rate. You will obtain $1929.70 after 10 years. The total amount that you put into the bank is $1593.74, so you will obtain the total interest of $335.95 over 10 years.


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