example 1: you have always wanted a bugatti. you find one for $3,000,000 and put a 10% down payment. you…

Explanation:

Step1: Calculate down - payment

The down - payment is 10% of the car price. The car price is $3000000. So the down - payment is $3000000\times0.1$. $3000000\times0.1 = 300000$

Step2: Calculate loan amount

The loan amount (PV) is the car price minus the down - payment. So $PV=3000000 - 300000=2700000$. The number of periods (N) is $6\times12 = 72$ months, the annual interest rate $r = 5.3%=0.053$, so the monthly interest rate $i=\frac{0.053}{12}$. The future value $FV = 0$. $P/Y = 12$ (payments per year) and $C/Y = 12$ (compounding periods per year). We use the formula for the present value of an ordinary annuity $PV = PMT\times\frac{1-(1 + i)^{-N}}{i}$. $PMT=\frac{PV\times i}{1-(1 + i)^{-N}}=\frac{2700000\times\frac{0.053}{12}}{1-(1+\frac{0.053}{12})^{-72}}$ Let $x=\frac{0.053}{12}\approx0.004417$. $PMT=\frac{2700000\times0.004417}{1-(1 + 0.004417)^{-72}}$ $(1 + 0.004417)^{-72}\approx0.7377$ $1-(1 + 0.004417)^{-72}\approx1 - 0.7377 = 0.2623$ $2700000\times0.004417 = 11925.9$ $PMT=\frac{11925.9}{0.2623}\approx45466.64$

Step3: Calculate total amount paid for the car

The total amount paid for the car is the down - payment plus the total of all monthly payments. The total of all monthly payments is $PMT\times N=45466.64\times72 = 3273598.08$. The down - payment is 300000. So the total amount paid is $300000+3273598.08 = 3573598.08$

Step4: Calculate total interest

The total interest is the total amount paid for the car minus the original price of the car. The original price of the car is 3000000. The total amount paid is 3573598.08. So the total interest is $3573598.08-3000000 = 573598.08$

Answer:

a. $300000 b. $45466.64 c. $3573598.08 d. $573598.08