# Future Value Money Formula, Calculation, and Example

Throughout the remainder of this book, we will focus on using the financial calculator to solve problems involving compound interest, instead of using the formulas as illustrated above. The more compounding periods there are, the greater the future value is going to be. The future value formula could be reversed to determine how much something in the future is worth today. In other words, assuming the same investment assumptions, \$1,050 has the present value of \$1,000 today. To understand the core concept, however, simple and compound interest rates are the most straightforward examples of the future value calculation.

You must apply a principle called the cash flow sign convention to the PV, PMT, and FV buttons. In the above scenario, you need to tell the employee the future value of their loan. The future value ([latex]FV[/latex]) is the accumulated value or maturity value of a loan or an investment at the end of the term of the loan or investment.

Whereas future value calculations attempt to figure out the value of something in the future, present value attempts to figure out what something in the future will be worth today. For example, assume a \$1,000 investment is held for five years in a savings account with 10% simple interest paid annually. In this case, the FV of the \$1,000 initial investment is \$1,000 × [1 + (0.10 x 5)], or \$1,500. You can use the future value formula to calculate how your current savings may turn into a home down payment, car down payment, or funds used to pay tuition. A financial calculator, like the TI BAII Plus, has built-in functions to solve compound interest problems.

## Future Value Calculations with Variable Changes

The future value includes the principal of the loan or investment plus all of the interest the loan or investment has accumulated over the term. The principal of the loan or investment is called the present value ([latex]PV[/latex]). The present value is the amount of money borrowed for a loan or the amount of money invested for an investment at the start of the term. You can use this future value calculator to determine how much your investment will be worth at some point in the future due to accumulated interest and potential cash flows.

1. For a perpetuity, perpetual annuity, the number of periods t goes to infinity therefore n goes to infinity and, logically, the future value in equation (5) goes to infinity so no equations are provided.
2. The “time value of money” states that a dollar today is worth more than a dollar tomorrow, so future cash flows must be discounted back to the present date to be comparable to present values.
3. Notice that nowhere on the calculator is there a button to enter this critical piece of information.
4. So the bond has increased from \$1,000 to \$1,485 after eight years, given the annual interest rate of 5.0% compounded on a semi-annual basis.
5. We can combine equations (1) and (2) to have a future value formula that includes both a future value lump sum and an annuity.

Let’s assume we have a series of equal present values that we will call payments (PMT) and are paid once each period for n periods at a constant interest rate i. The future value calculator will calculate FV of the series of payments 1 through n using formula (1) to add up the individual future values. Both concepts rely on the same financial principles (i.e. discount or growth rates, compounding periods, initial investments, etc.). Each component is related and inherently feed into the calculation of the other. For example, imagine having \$1,000 on hand today and expecting to earn 5% over the following year. You can calculate the future value of money in an investment or interest bearing account.

## Example Future Value Calculations:

However, if the interest compounds semi-annually, the investment is worth \$121 instead. For investors and corporations alike, the future value is calculated to estimate the value of an investment at a later date to guide decision-making. The Future Value (FV) refers to the implied value of an asset as of a specific date in the future based upon a growth rate assumption. Future value takes a current situation and projects what it will be worth in the future. For example, future value would estimate the value of \$1,000 today invested at 10% interest for 5 years. Alternatively, present value takes a future situation and projects what it is worth today.

Using the above example, the same \$1,000 invested for five years in a savings account with a 10% compounding interest rate would have an FV of \$1,000 × [(1 + 0.10)5], or \$1,610.51. Investing in alternative assets involves higher risks than traditional investments and is suitable only for sophisticated investors. Alternative investments are often sold by prospectus that discloses all risks, fees, and expenses. They are not tax efficient and an investor should consult with his/her tax advisor prior to investing. The value of the investment may fall as well as rise and investors may get back less than they invested.

It may be useful for an investor to know how much their investment may be in five years given an expected rate of return. This concept of taking the investment value today, applying expected growth, and calculating what the investment will be in the future is future value. What happens if a variable such as the nominal interest rate, compounding frequency, or even the principal changes somewhere in the middle of the transaction? When any variable changes, you must break the timeline into separate time fragments at the point of the change.

## Future Value: Definition, Formula, How to Calculate, Example, and Uses

The calculated future value is a function of the interest rate assumption – i.e. the rate of return earned on the original amount of capital invested, or the present value (PV). The future value of an annuity is the value of a group of recurring payments at a certain date in the future, assuming a particular rate of return, or discount rate. Continuing the calculations for each of the four compounding periods results in the following. When calculating future value of an annuity, understand the timing of when payments are made as this will impact your calculation. The concept of future value is often closely tied to the concept of present value.

## Continuous Compounding (m → ∞)

So the bond has increased from \$1,000 to \$1,485 after eight years, given the annual interest rate of 5.0% compounded on a semi-annual basis. The Internal Revenue Service imposes a Failure to File Penalty on taxpayers who do not file their return by the due date. The penalty is calculated as 5% of unpaid taxes for each month a tax return is late up to a limit of 25% of unpaid taxes. An additional Failure to Pay penalty can also be assessed, and the IRS imposes interest on penalties.

## What Is Future Value?

In other words, the \$500 tax obligation has a future value of \$525 when factoring in the liability growth due to the 5% penalty. A loan is charged interest but is usually paid off through payments, resulting in the principal decreasing over time. Notice that nowhere on the calculator is there a button to enter this critical piece of information.

Determining the future value of an asset can become complicated, depending on the type of asset. Also, the future value calculation is based on the assumption of a stable growth rate. If money is placed in a savings account with a guaranteed interest rate, then the future value is easy to determine accurately. However, investments in the stock market or other securities with a more volatile rate of return can present greater difficulty.