Answer to Question #278486 in Financial Math for Jayem

Question

A brand new car has a list price of Ᵽ850,000.00. The car dealer is giving a trade discount of 10% and

requires a 20% down payment. The car dealer has an arrangement with a bank to finance the balance on the

car. The term of the loan is 5 years. The bank is charging an interest of 6% per annum.

a. Compute the net invoice price of the car.

b. Compute the down payment needed and the balance that will be financed by the bank.

c. How much will the monthly payment be? What portion of the monthly payment for the first month will go

to interest and principal? What about the second monthly payment?

Answer 1

a. Compute the net invoice price of the car.

$=$ (1-trade discount)$\times$ list price

$=(1-0.1)\times P850,000$

$=P765,000$

b. Compute the down payment needed and the balance that will be financed by the bank.

Downpayment;

$=(0.2)\times P765,000$

$=153,000$

Balance that will be financed by the bank;

$=P850,000-P765,000$

$=P85,000$

c. How much will the monthly payment be? What portion of the monthly payment for the first month will go

Monthly portion;

$A=P(1+rt)$

$A=P765,000(1+0.06\times5)=P994,500$

Monthly payment would be;

$\frac{P994,500}{5\times12}=P16,575$

Portion that would go to interest and principal;

First month

A=P(1+rt)

$16,575=P(1+0.005)$

Principal will be;

$P=16492.5$

Interest will be;

$P16575-P16492.5=P82.5$

2^nd month

A=P(1+rt)

$(P16575\times2)=P(1+0.01)$

$P=\frac{33,150}{1.01}=P32,821.8$

Principal would be;

$P32,821.8$

Interest would be;

$P33,150-P32,821.8=P328.2$