What’s in the future value calculation?

We may use the future value calculator to compute the future value (FV) of an investment given the compounding term (N), interest/yield rate (I/Y), beginning amount, and monthly deposit/annuity payment per period inputs (PMT). The future value of a savings amount or investment is its value at a specified time or date in the future. In general word terms, we have:

FV = Present value + (Present value × Interest rate) or

FV = Present value × (1 + Interest rate).


Future value annuity formula derivation

The future value of an annuity is the worth of equally spaced payments at some time in the future, similar to the future value and present value of a dollar, which is the future value and present value of a lump-sum payment. The present value of an annuity is the present value of future payments that are equally spaced.

An annuity’s future value is just the sum of the future values of each payment.

FVAD = A(1 + r)1 + A(1 + r)2 +…+ A(1 + r)n

Future value growing annuity formula derivation

The future value of a rising annuity formula is used to compute the future amount of a sequence of cash flows or payments that rise at a proportional rate. An expanding annuity is another name for a growing annuity.

FV_{GA} = P \bigg[\frac{\big(1+r\big)^n - \big(1+g\big)^n}{r-g}\bigg]

  • P is first payment,
  • R is the rate per period
  • G is the growth rate
  • N is the number of periods

Future value definition

The worth of a present asset at a future date based on an expected growth rate is known as future value (FV). Investors and financial planners care about future value because it helps them predict how much an investment made now will be worth in the future. Knowing the future worth allows investors to make good investment selections based on their projected requirements. External economic variables, such as inflation, might, on the other hand, harm the asset’s future worth by degrading its value.

What is money?

Money is an institutionalized asset that a creditor under a social convention or legal obligation accepts to take from a debtor to cover his obligations that may arise from various transactions; specific measure and bearer of value generally acceptable in the exchange of goods and services. Because every day the value of money is becoming more important. Also, it’s one of the necessary factors for human life. Since we have a limited supply in the commodity market, money serves as an intermediary.

For money to qualify as money, it must meet certain norms. And that is to be a means of storing value: to possess an asset to store values ​​for a future purchase. There are no perishable goods of this quality. One of the most important norms is money as a means of exchange. To have some good, we have to exchange it. And the third norm is the unit of account. This means that to value a certain good, we use money as a property of the unit of account.

Money through history

The classical Latin name for money, pecunia (from pecus: cattle, treasure), is reminiscent of the time when cattle. In primitive commodity exchange, served as natural money; such an exchange of goods is present in many archaic peoples. Until recently, in the original (primitive) peoples, regarding the livestock, the means of payment were glass grains, cowrie snails, shells, etc. In developed civilizations, natural exchange was suppressed early by metal money, and precious metals were especially valued. In that oldest period of the appearance of coins, lumps, rods, or metal objects had to be weighed repeatedly to determine their mass and, according to it, their value (such as, for example, the Roman as ore).

Many ancient and modern names of monetary units preserve the memory of this developmental stage. Egypt had such money (gold and copper rings) until the time of Alexander the Great. In the next phase, the money got a specific shape and size, i.e. mass. The oldest such money appeared in Crete before 1500 BC. Kr. in the form of golden bull’s heads and golden. I.e. copper bars in the form of skinned animal skins with a mass mark.

Functions of money

Given the multitude of forms in which it historically occurs, we define money through its functions. I.e. money is considered to be what can perform the functions of money. Money has four essential functions. It serves as a unit of account, as a means of exchange, to preserve value and transfer value.

The time value of money

The idea of the time value of money (TVM) states that an amount of money is worth more now than it will be at a later period due to its earning potential in the interim. This is a fundamental financial principle. A sum of money in one’s hand is worth more than the identical sum paid in the future. The present discounted value of money is another name for the time value of money.

Because a quantity of money, once invested, rises over time, investors prefer to get money today rather than the same amount of money in the future. Money placed into a savings account, for example, receives interest. The interest is added to the principle over time, generating more interest. That is the power of compounding interest in action.

Unit of account

Money is a unit of account or a measure of value because it shows an economic good or service. It allows participants in economic transactions to compare the relative values ​​of different goods and services.

Medium of exchange

Money serves as a means of exchange because market participants are willing to accept it as a means of payment. They can sell their products for money and use that money to buy other products and services. As a means of exchange, money enables the division of labour and specialization because it allows people to produce only one type of goods or services and buy other goods and services for the money obtained from their sale.

Preserving value

Money is also a means of preserving value because its nominal amount remains unchanged as long as it is kept and enables us to preserve our goods and services by exchanging them for money. Which could eventually lose either its total value or some part of it. Thus, holding money allows for the interregional and intertemporal transfer of purchasing power.

Transferring value

The fourth function of money is transferring value to another subject to repayment at some future point (credit). Namely, money enables the value of deferred payments to be expressed, i.e. debts. The debt is later settled by some monetary means of exchange, i.e. the amount of contracted monetary units. The definition of money is most often through its function and that is the medium of exchange. Regardless of their physical form can perform other functions of money.

Money as medium of exchange (any amount)

The value of money

The time value of money, also called discounted value, is a financial formula that calculates the value of a certain amount of money that should be applied in the future, being reduced to the present value of that amount. It represents the calculation of the amount that must be invested today to equalize the payment. I.e., the amount to be applied in the future. This process is based on the time value of the money principle. Which says that $ 1 today is worth more than $ 1 tomorrow. For three reasons, today’s money is worth more than tomorrow because of: inflation, interest, and opportunity costs. Inflation, deflation, devaluation, and revaluation are changes in the value of money. Inflation is an increase in money circulation that increases the general level of prices. The amount of money changes regardless of the corresponding changes in goods.

The opposite of inflation is deflation, which is a disturbance in the balance of economic factors, manifested through the imbalance of commodity-money relations, resulting in a decline in the general price level. It represents a real reduction in the value of money and a reduction in purchasing power. One of the acts of monetary authority is devaluation. It represents a change in the value of money on an interval basis. That is the reduction of the value of money concerning the standard, i.e., the legal reduction of the interval value of the domestic currency. Revaluation is a legally enforced increase in the value of the domestic currency against its standard.

How it looks in practice

Would you rather have $ 1,000 today or $ 1,000 in a year? Of course, we want to have $ 1,000 today. If we have $ 1,000 today, we can spend it immediately, but we can also save it to make money on it in those years through interest, stocks, business, or other assets whose value is growing. If we waited for that $ 1,000 for a year instead of taking it right away, we would have lost profits. That is, we would create an opportunity cost – everything we could do and earn with them, but we didn’t. There is also inflation that $ 1,000 is worth more today than in a year. If inflation is 2% per year, it is $ 19.61, so we would have $ 980.39 in purchase value.

Money that stands unused is eaten up by opportunity cost and a debilitating factor of inflation. For that reason, financial experts tell companies that the financial obligation is over, and companies that keep a lot of bags in their accounts are inefficient.

Whether we would make $ 1,000 today or $ 1,500 in a year, we know we would choose that figure of $ 1.5,000 in one year. What this amount depends on is the interest rate. If we invest $ 100 per 10% after a year we will have $ 110 (100 * 1.10 = 110). This is a calculation for the first year, and for all working years, we calculate the same. What if we want to calculate in 30 years? It is hard to calculate and add each year separately. Instead, we will use the formula:

FVn = PV * (1 + k) n

Time value calculation

A compound interest account

The present value of future cash flows is calculated using the discounting technique, the future value of current cash flows is calculated using the interest rate technique.

Using the interest or discount rate

The rate at which investors are willing to invest in a financial instrument or another asset, the risk-free interest rate, and the risk premium as valued by the average investor

Present and future value

The present value determines the cash flow value that will receive in the future in today’s dollars. Discounts on the current date of future cash flow, using the number of periods and the average rate of return. Regardless of the present value, if that value is invested in the present value at the rate of return and the number of specific periods, the investment will grow to future cash flow.

The future value determines the cash flow value received today in the future, based on interest rates or capital gains. Calculate the value of current cash flow in the future, if it is invested by the rate of return and the number of specific periods. Both present and future value take into account compound interest or capital gains. This is another crucial aspect that investors should consider when looking for a good investment.

Example 1 – Calculating the future value

For example, the first bank accepts your $ 1,000 deposit now, adds $ 80 at the end of one year, retains the $ 1,080 for the second year, and pays you interest at an 8 percent rate. The bank returns your initial deposit plus accumulated interest at the end of the second year. How much will you receive as a future value?

Future value = Present value × [(1 + Interest rate) × (1 + Interest rate)]

For our two-year investment example, we have,

Future value = $1,000 × (1.08) × (1.08)
1,000 × 1.1664
= $1,166 (rounded)

Example 2 – Calculating the present value

Assume you have the option of receiving $ 2,000 now at a 3 percent annual rate of $ 2,200 one year from now. Which choice is the best?

Using the present value method, the computation is $ 2,200 / (1 +. 03)1 = $ 2135.92 PV = $2135.92, or the minimal amount spent today to get $ 2,200 one year from tomorrow. In other words, if you were given $ 2,000 today with a 3% interest rate, it would not be enough to provide you $ 2,200 a year later.

Alternatively, you could determine the future worth of the $ 2,000 today in a year by multiplying it by 1.03: 2,000 x 1.03 = $ 2,060.

Limitations of the future value calculator

The future value calculations are estimations of the future worth of an investment. Future value estimations may be deceptive in the following situations:

  • The future value may not provide a correct response if interest rates fluctuate fast because it is only sensitive to interest rate changes if they remain constant during the selected time period.
  • The buying power of future cash flows is diminishing in an inflationary economic environment. Future value calculations are simply an approximation in this situation.
  • Future value computations may not correctly reflect the real worth of an investment if currency values fluctuate.

How to double your money? – the Rule of 72

The Rule of 72 is a simple approach for an investor or adviser to estimate how long it will take to double an investment based on its fixed yearly rate of return. Divide 72 by the fixed rate of return to understand how long it will take for your portfolio to double in size. However, the science isn’t perfect, and you may want to use a different calculation to account for rates of return that fall outside of a specific range. Both of these general rules of thumb can assist investors in comprehending the potential of compound interest. The higher the rate of return, the less time it takes to double or triple an investment.


How to calculate the future value?

The future value formula is FV=PV(1+i)n, where the present value PV rises by a factor of 1 + I for each period into the future.

How do you calculate the future value of a series of deposits?

If you deposit $100 at the end of one year with a 5% interest rate and the number of years is one, the calculation is as follows. At the end of one year, the future value (FV) equals the present value ($100) plus the value of the interest at the stated interest rate (5 percent of $100, or $5).

Why do you need to calculate future value?

Investors and financial planners care about future value because it helps them predict how much an investment made now will be worth in the future. Knowing the future worth allows investors to make good investment selections based on their projected requirements.

What two methods are used to calculate future values?

Because of market volatility, determining the FV of a market investment can be difficult. There are two methods for determining an asset’s FV: simple interest and compound interest.

Other calculators

Be sure to check out our Present Value Calculator to find out how to calculate the present value of money.
You can also find out what the difference is between net present wave and present value and how each of them is calculated. Of course, if you are curious and if you want to know something more about the time value of money, even look at a few examples of calculating PV and NPV, but also check this PVIFA Calculator as well.
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