Lessons · Accounting · present value of one sum
Present value of one sum
Money later is worth less than money now, because money now could be earning. The present value of a future sum is that sum divided by (1 + rate) once for every period you wait: PV = FV / (1 + r)^n.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A customer offers 11,000 in two years or 10,000 today, and the owner asks which is more. The answer depends on what money earns, and the calculation tells the owner exactly where the line is.
How to think about it
Write the future sum, the rate per period and the number of periods. Raise (1 + rate) to the number of periods. Divide the future sum by that. Compare the result with the money on offer today.
Worked example
FV 11,000, r 5% per year, n 2 yearsThe three inputs.
(1 + 0.05)^2 = 1.1025Two years of growth, compounded.
PV = 11,000 / 1.1025 = 9,977.32What 11,000 in two years is worth today at 5%.
9,977.32 < 10,000 → take the 10,000 nowThe later sum is worth less than the money on the table.
Your turn
9,000 in three years at 4%. Write the line with the exponent filled in.
PV = 9,000 / (1 + 0.04)^
Solve one, graded on the server
The trap
Multiplying instead of dividing. 11,000 × 1.1025 is 12,127.50, which is what 11,000 today would grow to, the opposite question.