# How to calculate savings over the life of a car loan?

I'm working through the maths in this, only the relevant parts of which I quote:

...On a \$25,000 car loan through the manufacturer for four years, your monthly payment would be about [1.] \$520 at 0% interest or [2.] \$541 with a 1.9% interest rate.$1. = 25000/48 \text{ months } = \$520$.

I think that I need this formula : $\text{Monthly Payment} = PV \times \dfrac{R}{[1 - (1 + R)^{-n}]} \qquad (♦)$
where PV = Present Value (beginning value or amount of loan),
R = Periodic Interest Rate
n = # of interest periods for overall time period

$2.$ $PV = 25,000, \quad R = 1.9\%/12 = 0.019/12, \quad n = 48 \text{ months}$.

If you opted for the manufacturer rebate and a five-year loan term through a bank or credit union, you'd spend more on interest but your monthly payment would be substantially lower than the four-year manufacturer loan. For example, with a \$2,500 manufacturer's rebate, you'd lower your financed amount to \$22,500. [3.] At a $5\%$ interest rate, your monthly payment would be \$424, [4.] while at a$4\%$interest rate your monthly payment would be about \$414.

$3.$ Just use the formula $(♦)$. $PV = 22,500, \quad R = 5\%/12, \quad n = 60 \text{ months}$.
$4.$ Same as $3$, but $R = 4\%/12$.

...On a \$25,000 car with a choice of a \$2,500 rebate or 1.9% financing over five years, it's a better deal to take the manufacturer rebate and get financing elsewhere. At a 4 percent interest rate with the \$2,500 rebate, you'd save$\color{darkred}{ [5.] \; \$1,364 }$ in total payments. With a 5 percent loan rate with the \$2,500 rebate, you'd still save$\color{darkred}{ [6.] \; \$750 }$ over the life of the loan.

$I.$ Would someone please explain how to calculate the red $\color{darkred}{5, 6}$?
$II.$ Based only on the given info, how would you know that to calculate $R$, the given interest rates must be divided by 12?

I: It looks like they get 5 and 6 by taking the cash rebate from the price of the car and calculating the interest on that lowered value (\$22,500 instead of$25,000). Not sure why you couldn't just put it towards the price of the car at the dealership and get the 1.9%, but oh well.
In other words, calculate 1.9% for 5 years on \$25,000, compare to 4% for 5 years on \$22,500 and 5% for 5 years on \$22,500 and you should get those values in 5 and 6.