Lessons · Engineering · present and future value
Present and future value: money moved through time
A sum P today becomes F = P (1 + i)ⁿ in n periods; a sum F due in n periods is worth P = F / (1 + i)ⁿ today.
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 pump will need a $12,000 rebuild in five years, and the question is how much to set aside now. Dividing by the growth factor gives it, and putting that number in the budget today is what a maintenance plan actually is.
How to think about it
Forward in time, multiply by (1 + i)ⁿ. Back in time, divide by it. If the present value you got is bigger than the future sum, the exponent went the wrong way.
Worked example
F = P (1 + i)ⁿ forward; P = F / (1 + i)ⁿ backThe same factor, used in both directions.
A pump will need a $12,000 rebuild in 5 years. Money earns 6 %The setup.
P = 12,000 / 1.06⁵ = 12,000 / 1.3382 = $8,967Divide by the growth over five years.
Put $8,967 aside today and it is $12,000 on the day the rebuild is dueWhat the number means.
Your turn
$5,000 due in 3 years at 5 %. Write the present value.
P = 5000 / 1.05^ = $4,319.19
Solve one, graded on the server
The trap
Multiplying when going backwards. Present value shrinks. If the number you got is bigger than the future sum, you compounded instead of discounting.