CALCULATE

CALCULATE

** Present value calculator** uses three values, future value, interesting rate and time periods, and calculate the present value of a certain amount of money. It is an online a financial tool requires three positive real numbers, future value interesting rate and time periods to determine the amount of money needed to invest today in order to have a specified balance in the future.

It is necessary to follow the next steps:

- Enter three values for future value, interesting rate and time period in the box. These values must be positive real numbers;
- Press the
**"CALCULATE"**button to make the computation; - Present value calculator will give the present value of a stream of cash flows.

The present value is determined by the following formula

$$PV=\frac{FV}{(1+r_t)^n}$$ where $FV$ is the future value, $r_t$ is the interest rate and $n$ is the number of periods.

$$PV=\frac{FV}{(1+r_t)^n}$$ where $FV$ is the future value, $r_t$ is the interest rate and $n$ is the number of periods.

In economics and finance, a basic unit of account is a set of future cash flows. Cash flows have two important properties: amounts and dates at which the amounts are paid. Let us consider, for example, a cosmetic company about to start making products in a new area. The cosmetic company is facing uncertainty at several levels. There is uncertainty about whether the company actually finds the good raw material of production. Even if they find raw materials, there is a lot of uncertainty about what price they can sell their products. In this case, it is difficult to find the future cash flows, the best one can do is to estimate the expected future cash flows.
By $X_t$ we denote the amount $X$ to be paid at a future date $t$.
If the set of dated cash flows is given, we can define its Present Value (PV) as its value today. The Present Value is the sum of the values of the individual dated cash flows. So, we use the set of prices $P_t$ today of receiving $\$1$ at time $t$ in the future. Therefore,
$$PV=\sum_{i=1}^{n}P_iX_i$$
For each price $P_t$ there is a corresponding interest rate $r_t$. The relation between the prices $P_t$ and interest rates $r_t$ are given by the following formula:
$$P_t=\frac 1{(1+r_t)^n}$$ The interest rate is the change, expressed as a percentage, in the amount of money during one period of time. The period can be annually, semi-annually, quarterly, monthly, or daily.

There are several types of interest rates:

- Compound interest when the interest that increases exponentially over subsequent periods;
- Simple interest, that does not increase;
- Nominal annual interest, the simple annual interest rate of multiple interest periods, etc.

To determine a present value, it is necessary to follow the next steps:

- Find the future value;
- Find a periodic rate of interest;
- Find the number of periods;
- Divide the future value by $(1+\mbox{rate of interest})^{\mbox {periods}}$
- Simplify the result if needed.

Present Value is an important factor in the time value of cash, which forms the backbone of accounting and finance. It is applicable in mortgages, auto loans, credit cards, etc.

**Practice Problem 1 : **Find the interest rate which is needed to grow $\$150$ to $\$180$ in three years.

**Practice Problem 2 : **Find an amount of money that Ann will have in a account if he saves $\$2,500$ at $3.5\%$ interest for $5$ years.

The present value calculator, formula, real world problems and practice problems would be very useful for grade school students (K-12 education) to understand the concept of an investment of money. This concept can be of significance in almost all fields of accounting and finance. For students, which want to be investors, business owners or decision makers in future, the time value of money is a critical concept and needs to be understood.