**Question:**How to Calculate the Future Value of an Investment

There are three approaches to solving the problem of calculating the future value of an investment, one type of time value of money calculation calculation. First, you can use the future value of a lump sum formula. Second, you can use a financial calculator. Just about any financial calculator will do and will follow just about the same steps. Third, you can use a spreadsheet, such as Excel. We will explore all three approaches.

**Answer:**

**The Problem and The Formula**

Let's say we have $100 and the interest rate is 5%. The year (t) is year 1. Using the **future value of a lump sun formula**, we can calculate the future value of $100 if the interest rate is 5% at the end of 1 year:

**FV _{1} = PV + INT = PV(1 + I)^{t} = $100(1 + 0.05) = $105**

so if you make an investment of $100 at an interest rate of 5% and hold it for 1 year with no other deposits and no withdrawals, you will have $105 at the end of the year.

This begins a step-by-step approach. To calculate the future value of the lump sum for year 2, you can use the following approach. You begin Year 2 with $105 so:

**FV = $100(1 + 0.05) ^{2} = $110.25**

You have just run into what is called compounding of interest. More interest is earned in the second year because interest is calculated on both the interest and the principal from year 1. You can continue to use this formula to find the future value of the investment by calculating this formula for years 3 and beyond.

**Future Value of an Investment Using a Financial Calculator**

**The formula for finding the future value of an investment is:**

**FV _{N} = PV(1 + I)^{t}**

You can use this formula to calculate future values with any calculator with an exponential function, even non-financial calculators. It is best to use financial calculators because they have five keys that correspond to the five variables in time value of money equations. This future value of an investment equation that we calculated above uses only four of those variables. Look at your financial calculator. Here are the key and inputs that you punch:

Punch **N** and **2** (for 2 years)

Punch **I/YR** and **5** (for the interest rate of 5%)

Punch **PV** and **-105** (for the amount of money we are calculating interest on in year 2)

Punch **PMT** and **PMT** (there are no payments beyond the first one)

Punch **FV** and **you will have your answer of $110.25**

**Future Value of an Investment Using a Spreadsheet**

Spreadsheets, such as Microsoft Excel, are suited for calculating time value of money problems and other mathematical functions. The function that we use for future value of an investment or a lump sum on an Excel spreadsheet is:

**=FV(0.05,1,0,-100,0)**

Specifically, you go to an Excel worksheet and click on Financial function. You will pull down a menu and click on FV. That will open a box and you will fill out the information for the problem you are trying to solve. In the example we are using, you fill out the interest rate of 0.05, the time period of 1 (year), payments of 0, present value of $100 expressed as a negative number, and a 0 for the last item which means that any payment would be at the end of the time period if we had payments. You end up with the function above. Then, you go to the right-hand side of the worksheet at the top and click on Calculate. You will get the answer of $110.25.

This video lesson will help you with practicing calculations for future value of an investment.

These are the three ways to calculate future value of an investment or lump sum if no withdrawals are made during the time period and no deposits are made.