Question

. Let's take some practical situation and apply the basic math skills to find the answer (just warming up before getting to statistics).
You are buying a car. Dealer want you to pay some Down Payment (D) now and the rest of the money month-by-month (M - monthly payment) during next five years (no interest).
If P is the price of the car, then we can make an equation:
P = D + M*12*5      or     P = D + 60*M
Assign your own values for Price of the car you want to buy, Down Payment you can make, and find your Monthly Payment.
What car would you like to buy (don't worry about money now).

Answer 1

Here we will be looking at 2 examples of the prices, price of the car being equal in both the cases and then having 2 different combinations of the down payment and the month - by - month payment.

Let the price of the car in both cases be 10,000

• First case is when the down payment is 4000, then the monthly payments would be computed using the equation as: 10,000 = 4,000 + 60M which means that 60M = 6,000 and therefore M = 100 . Therefore here we have the down payment D = 4000 and M = 100 as the monthly payment.
• Second case is when the down payment is 1000, then the monthly payments would be computed using the equation as: 10,000 = 1,000 + 60M which means that 60M = 9,000 and therefore M = 150 . Therefore here we have the down payment D = 1000 and M = 150 as the monthly payment.

Now we know that with time the value of the money increases ( at a risk free rate ) . Therefore we would prefer to give a lower down payment than a higher down payment. Therefore we are likely to buy a car with the second combination of down payment = 1000 and monthly payment as M = 150

Note that this could also be understood by the fact that the extra down payment of 3000 in the first case could have been kept in the bank to earn a risk free rate.