Formula for the present value (discounted value) of a future amount

P = the present value of amount A, due n years from now

r = the rate of interest

For example, someone contracts to pay you $100,000 in ten years. What's that worth right now, if they changed their mind and decided to paid you upfront? Say the interest rate is 5%.

At simple interest:

P = A/(1 + nr)

If A = 100,000 and n = 10 and r = 0.05 (which is to say, 5%), then

P = 100,000/(1 + 10x0.05) = 100,000/1.5 = 66,667

At interest compounded annually:

P = A/(1 + r)ⁿ

Using the same example as for simple interest, this gives

P = 100,000/(1 + .05)¹⁰ = 100,000/1.62889 = 61,391

At interest compounded q times a year:

P = A/(1 + r/q)^nq

Or in the same example but compounding monthly (q = 12)

P = 100,000/(1 + 0.05/12)¹²⁰ = 100,000/1.64701 = 60716