Relationship between the Present and Future value of a single amount of money ▪ Let 𝑃 and 𝐹 be the present (current time period) and future (i.e. time period 𝑛) value of a single amount assuming interest rate will remain at 𝑖% per period within the entire time period considered. Then, 𝑃 and 𝐹 are related by the formula: 𝐹 = 1 + 𝑖 𝑛 ▪ Note that this formula is for a single amount, and 𝑛 is the number of periods from the future period to whatever present time in mind. ▪ Usually, the present is time zero. However, there will be instances where for purposes of calculation sake one could assume say, time period 3 as the present, and later consider time period 3 as the future to be taken to time zero. This will become clear later.

The relationship between the Present and Future value of a single amount of money is determined by the formula 𝐹 = 𝑃(1 + 𝑖)^𝑛. Here, 𝑃 represents the present value of the money, 𝐹 is the future value, 𝑖 is the interest rate per period, and 𝑛 is the number of periods.

This formula is used when we want to find out how much a certain amount of money today will be worth in the future if it grows at a certain interest rate. The interest rate is assumed to remain constant over the entire period.

The present time is usually considered as time zero. However, for calculation purposes, we can assume any time period as the present. For example, we can consider time period 3 as the present, and later consider time period 3 as the future to be taken to time zero. This concept will become clearer as we apply it in different scenarios.

The relationship between the Present and Future value of a single amount of money is determined by the formula 𝐹 = 𝑃(1 + 𝑖)^𝑛. Here, 𝑃 represents the present value of the money, 𝐹 is the future value, 𝑖 is the interest rate per period, and 𝑛 is the number of periods.

Step 1: Identify the present value (𝑃), the interest rate (𝑖), and the number of periods (𝑛).

Step 2: Add 1 to the interest rate (𝑖).

Step 3: Raise the result of step 2 to the power of the number of periods (𝑛).

Step 4: Multiply the present value (𝑃) by the result of step 3. The result is the future value (𝐹).

This formula assumes that the interest rate will remain constant over the entire time period considered. It's also important to note that this formula is for a single amount, not for a series of payments or receipts.

In some cases, for calculation purposes, a different time period may be considered as the present. For example, time period 3 could be considered as the present, and later, time period 3 could be considered as the future to be taken to time zero. This concept will become clearer as you gain more experience with these calculations.