The Time Value of Money is a foundational concept in finance. This term refers to how much a dollar is worth today compared to what the dollar would be worth at some point in the future. A dollar today is worth more than a dollar tomorrow because of inflation.
Inflation is the growth of the money supply. Due to laws of supply and demand, money becomes worth less as time goes on because the money supply is always growing.
Deflation is the opposite of inflation. Deflation is the shrinking of the money supply, which makes money more valuable because it is scarcer.
Here’s an illustration of these concepts:
How do financial professionals deal with the time value of money since money is slowly losing its value as time progresses? One strategy is interest rates.
Interest rates are percentages that are charged on sums of money. When borrowing money, during the payback period, the borrower has to pay more than the borrowed amount due to the interest rate. This interest rate accounts for the time value of money because the lender is taking a risk with the borrower and wants to be paid back accordingly, taking into account the rate of inflation.
Here’s an illustration of these concepts:
Discount rates are similar to interest rates but are slightly different. Whereas an interest rate is charged at the end of a period, the discount rate is charged at the beginning of the period. The lender makes more money from a discount rate than from an interest rate because with a discount rate, the borrower must instantly pay back a portion of the borrowed money without being able to use it even though they are being charged interest on that portion of the money.
Because the discount rate is different from the interest rate, a unique formula is needed to calculate the discount rate:
Here’s an illustration of these concepts:
As you can see, it’s better to pay back the amount after one time period because of the discount rate. If the bank had waited to pay back the amount once the second time period had begun, they would have paid more than the final amount.
There are different types of interest rates. Most of the time, you will encounter nominal interest rates. However, this is not the true interest rate. Instead, the effective interest rate is the real interest rate. APY or APR is a type of effective interest rate.
The reason why a nominal interest rate is not the real interest rate is because, when multiplied by the principal amount, it does not provide the exact number. Instead, the effective interest rate allows you to calculate the true amount owed. The same can be said for the nominal discount rate versus the effective discount rate.
Here are the formulas for converting interest rates and discount rates:
In finance, v notation is sometimes used as shorthand for operating with complex formulas. These are the various formulas for v:
As you can see, there are also special relationships among v, interest rates, and discount rates. The summation of v and d is equal to 1. Also, there is a difference between v and the reciprocal of v. Regular v is used in present value calculations while the reciprocal of v is used in future value calculations.
When charging interest, the starting amount of money is known as the principal. There are two basic methods for charging interest: simple and compound. Simple interest is only charged on the principal. Compound interest is different from simple interest because compound interest charges interest on both the principal and the previously accrued interest. These are the formulas for simple interest and compound interest:
Here's an example problem to demonstrate the differences between simple and compound interest:
As you can see, while the simple interest yielded more money in the end, it took twice as long. If the compound interest were to extend beyond 5 years, it would yield substantially more. Thus, depending on the investor’s goals, compound interest will yield more in a shorter amount of time because compound interest is charging interest on previously accrued interest. This stands in contrast to simple interest, which only charges interest on the original principal.
