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?