Time Value of Money Calculations: Videos & Practice Problems

The time value of money (TVM) is a financial concept that states money available today is worth more than the same amount in the future due to its potential earning capacity. This principle is crucial because it underpins many financial decisions, such as investments, loans, and savings. By understanding TVM, you can make informed choices about where and when to allocate resources to maximize returns. For example, investing $1,000 today at a 5% annual interest rate will grow to $1,276.28 in five years, illustrating how money can grow over time.

To calculate the future value (FV) of an investment using the time value of money formula, you use the equation:

${\mathrm{FV}}_{}={\mathrm{PV}}_{}(1+r_{})n^{}$

Here, ${\mathrm{FV}}_{}$ is the future value, ${\mathrm{PV}}_{}$ is the present value, $r_{}$ is the interest rate per period, and $n^{}$ is the number of periods. For example, if you invest $1,000 at an annual interest rate of 5% for 3 years, the future value would be:

${\mathrm{FV}}_{}=1000(1+0.05)3^{}=1157.63$

Compounding and discounting are two fundamental concepts in the time value of money. Compounding refers to the process of determining the future value of a present amount of money by applying interest over multiple periods. It involves earning interest on both the initial principal and the accumulated interest. For example, investing $1,000 at a 5% annual interest rate will grow to $1,276.28 in five years.

Discounting, on the other hand, is the process of determining the present value of a future amount of money by removing the interest that would have been earned over the periods. It helps in understanding how much a future sum is worth today. For instance, $1,000 to be received in five years, discounted at a 5% annual rate, is worth $783.53 today.

A timeline is a helpful tool to visualize cash flows in time value of money calculations. It allows you to map out the timing of cash inflows and outflows over different periods. To create a timeline, draw a horizontal line and mark the periods (e.g., years, months) along the top. Below the line, indicate the cash flows at each period. For example, if you invest $100 today at a 10% interest rate for 3 years, your timeline would have:

Year 0: -$100 (initial investment)

Year 1: $0 (no cash flow)

Year 2: $0 (no cash flow)

Year 3: $133.10 (future value of the investment)

This visualization helps in understanding the timing and magnitude of cash flows, making it easier to apply TVM formulas.

The key variables in the time value of money equation are:

${\mathrm{FV}}_{}$: Future Value - the amount of money in the future.

${\mathrm{PV}}_{}$: Present Value - the current amount of money.

$r_{}$: Interest Rate - the rate at which money grows per period, expressed as a decimal.

$n^{}$: Number of Periods - the total number of time periods (e.g., years, months) over which the money is invested or borrowed.

These variables are used in the formula:

${\mathrm{FV}}_{}={\mathrm{PV}}_{}(1+r_{})n^{}$

to calculate the future value of a present amount of money, considering the interest rate and the number of periods.