 # Money in time: Relationship between Future Value and Present Value To talk about money in time, or the relationship between Future Value and Present Value, let’s start by answering 2 questions:

1. Would you rather receive \$10,000.00 today or \$10,200.00 a month from now?
2. Would you rather receive R\$10,000.00 today or R\$1,000,000.00 in 20 years?

To answer these questions, you must consider numerous factors, but one thing is certain: you would definitely prefer 10,000 today than the same 10,000 a month from now! This brings us to a fundamental principle of finance:

• Present Value: equivalent to the value it has today, in our example R\$10,000.00.
• Future Value: equivalent to a value greater than the value it has today, in our example the values ​​of R\$10,200.00 in a month or R\$1,000,000.00 in 20 years.

The updating of money over time is called the interest rate. It is the interest rate that will determine this relationship between Future Value and Present Value.

Now that we understand the concept of interest, we can explain how simple interest and compound interest work.

Simple interest: is when the interest rate is always applied on the initial balance. For example, if we take a loan of R\$1,000.00 for 10 months and consider a simple interest rate of 10% per month, we will have the same amount of R\$100.00 per month (10% of R\$1,000.00) for 10 months:

Compound interest: the so-called interest on interest, is when the interest rate is applied on the accumulated balance, that is, when the interest rate is applied on the initial amount in the first installment and in the second installment the interest is on the initial amount plus interest on the first installment, and so on. Using the previous example, of simple interest, and applying compound interest we have:

Mathematically speaking, the Future Value (FV) is the inverse function of the Present Value (PV) and vice versa. In fact, notice that the formula:

VP = TF/(1 + i) n

PV = VP*(1 + i) n

i=interest rate

n=period in which the money will be borrowed/invested

Thinking about these concepts, we understand that interest can either help or hinder. When we make an application or financial investment, interest is great for increasing the initial amount. Now, when we take out a loan-to-value ratio or financing, we must be careful that the initial amount does not snowball and get out of control due to the interest charged.

Therefore, be careful when making an overdraft, spending more money on your credit card than you can afford or applying for financing to buy a car. Everything has to be very well planned to not have financial problems.

Now that you understand the concept of the relationship between money and time, simple interest and compound interest, read the second chapter of our Investment Knowledge Trail in our next issue of the Newsletter. The article will be about the difference between Fixed Income and Variable Income.

So, did you like to know the differences between personal loans and financing? If you liked it, share it with the guys! 🙂  