Borrowing, Lending, and Interest
When someone borrows money for a year, the interest rate is the price, calculated as a percentage of the amount borrowed, charged by the lender.
Suppose that you are paid a bonus of $1,000 today, and you decide that you don’t want to spend the money right now. You put it in the bank; in effect, you are lending the $1,000 to the bank, which in turn lends it out to its customers who wish to borrow. At the end of a year, you will get more than $1,000 back—you will have the $1,000 plus the interest earned. All of this means that having $1,000 today is worth more than having $1,000 a year from now. As any borrower and lender know, this is what allows a lender to charge a borrower interest on a loan: borrowers are willing to pay interest in order to have money today rather than wait to have the money until they have saved it from their own income. When someone borrows money for a year, the interest rate is the price, calculated as a percentage of the amount borrowed, charged by the lender
What we will now see is that the interest rate can be used to convert future benefits and costs into what economists call their present values. By using present values when evaluating a project, you can evaluate a project as if all its costs and benefits were occurring today rather than at different times.
Defining Present Value
The key to the concept of present value is to understand that you can use the interest rate to compare the value of a dollar realized today with the value of a dollar realized later. Because the interest rate correctly measures the cost to you of delaying the receipt of a dollar of benefit and, correspondingly, the benefit to you of delaying the payment of a dollar of cost.
We’ll use the symbol r to represent the interest rate, expressed in decimal terms—that is, if the interest rate is 10%, then r = 0.10. If you lend out $X, at the end of a year you will receive your $X back, plus the interest on your $X, which is $X × r.
Amount received one year from now as a result of lending $X today
$X + $X × r = $X × (1 + r)
Example of Present Value
Let's say you have the choice of being paid $100 today or $110 one year from now. You also have the option of investing the $100 that'll earn a 5% rate of return over the next year. Which is the best option?
Using the present value formula, the calculation is $110 (FV) / (1 +0.5) ^1.
PV = $104 or the minimum amount that you would need to be paid today to have $110 one year from now. In other words, if you were paid $100 today and based on a 5% interest rate, the amount would not be enough to give you $110 one year from now. How do you calculate present value? Present value is calculated by taking the future cashflows expected from an investment and discounting them back to the present day. To do so, the investor needs three key data points: the expected cashflows, the number of years in which the cashflows will be paid, and their discount rate. PPF also plays a crucial role in economics. It can be used to demonstrate the point that any nation's economy reaches its greatest level of efficiency when it produces only what it is best qualified to produce and trades with other nations for the rest of what it needs. PPF is also referred to as the production possibility curve or the transformation curve.
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