**Interest Rates**

**by**

**Hieu Huy Nguyen**

Our goal is to explore the affects of simple interest and compound interest. The idea is to understand how monetary values change over time based on a given interest rate.

**Simple Interest **

Simple interest rates are non-compounding. This means that the interest rate is fixed and does not change based on the time period. Given a present value, we can determine the future value using the equation below:

FV = PV *(1+rt)

where PV is the present value, FV is the future value, r is the interest rate, and t is the time period.

With this equation, we can choose an arbitrary present value of $1,000 and observe the changes in future value as the t changes. The following changes were recorded on the spreadsheet below.

The results indicate that the interest remains constant (simple interest) throughout any duration of years. The future value is an example of the $1,000 worth after t number of years. This example can be connected to real world subjects such as savings. Due to inflation, many people create savings accounts, in which their deposits (principle amount) grow at the rate of which monetary growth occurs in the economy.

For **compounding interest**, the interest rate and the time period determines the growth rate. The growth rate indicates the effective interest rate that is compounded into each year. Thus, the interest rate changes as time changes. The equation for future value due to compounded interest rate is as follows:

FV = PV * (1+i)^t

where PV is the present value, FV is the future value, i is the interest rate, and t is the time period.

With this equation , we can again use the arbitrary present value of $1,000 and observe the changes in future value as t changes. The following changes were recorded on the spreadsheet below.

Notice that the future values for compounding interest is higher than simple interest as the years increase. This is due to the fact that the effective interest rate increases as the years increases; thus, this changes the growth rate, which is shown in the last column of the spreadsheet. In reality, simple interests are typically used for savings for consumers. However, when dealing with loans and debt, the majority of the time, companies imply the compound interest rate method in order to collect more value as the time period of borrowed money increase. In essence, the longer it takes for you to pay back money, the more youâ€™ll end up paying!!! Avoid DEBT!!

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