An interest rate (r) is the rate of return that equates the value of different cash flows on different dates.
If you have $1,000 today, you know what it is worth — $1,000. You can use it to purchase $1,000 worth of whatever you would like. However, what if you had the opportunity to receive $1,000 in 1 year? What would that be worth? Would you pay $1,050 now to receive $1,000 in 1 year? Probably not, because you could just keep the money and have $1,050 in one year (assuming it is not lost, stolen, or destroyed during that time.) However, if you could pay less than $1,000 today to receive $1,000 in the future the offer might be tempting. Perhaps you would be willing to spend $975 today to receive $1,000 in 1 year.
In this case, you can consider the value of waiting 1 year to be $25 ($1,000 – $975.) It can be expressed as an interest rate, r = 25/975 = 0.02564 or 2.56%.
This interest rate can be interpreted in three ways: as a required rate of return; a discount rate; or an opportunity cost.
The required rate of return is the minimum amount an investor would have to receive in order to make an investment worthwhile.
The discount rate is the rate at which a future cash flow must be discounted to determine its value today. For this reason, “discount rate” and “interest rate” are often used interchangeably.
Finally, the opportunity cost is what an investor must give up to receive the future payment. To get $1,000 in the future, the investor is unable to spend $975 today. If he had chosen instead to spend the money, he would have lost the opportunity for it to increase by 2.56%.
This post addresses a learning outcome covered in “The Time Value of Money.”