How to calculate a lease payment with a residual

A lease is a loan that isn’t paid down to zero, with payments made at the start of each month. That’s FV for the residual and BEG mode for the timing.

Problem

A $42,000 car is leased for 36 months at 6% a year, with a $25,000 residual value. Payments are due at the start of each month. What’s the payment?

Keystrokes

fFINx≷y
0.00
Start clean.
gBEG7
0.00
Payments at the beginning of each period. BEGIN lights up.
36n
36.00
The number of payments.
6g12÷i
0.50
Monthly rate.
42000PV
42,000.00
The value of the car you receive.
25000CHSFV
−25,000.00
The residual: the value you give back, or pay to keep the car.
PMT
−638.98
The monthly payment.
gEND8
−638.98
Back to the usual end-of-period payments.

Answer

The lease payment is $638.98 a month, before taxes and fees.

Why it works

You only pay for the part of the car you use up, $17,000 here, plus interest on the full $42,000 while you have it. FV tells the calculator that $25,000 of value is still there at the end.

gBEG7 matters: the first payment is due on day one, so each payment earns the lessor a month less interest, and the payment is a little lower than with payments at the end.

Money factor

Car leases often quote a money factor instead of a rate. Multiply it by 2,400 to get the annual rate: a money factor of 0.0025 is 6%.

Questions

Why switch back to END?

BEGIN stays on until you change it, and most loans pay at the end of each period. Leaving it on would quietly change your next answer.