Question

11. Samir wants to purchase his first car. He has saved $1000 as a deposit but the cost of the car is $5000.
Samir takes out a loan from the bank to cover the balance of the car plus $600 worth of on-road costs.

a. How much will Samir need to borrow from the bank?
$4600

b. Samir takes the loan out over 4 years at 9% p.a.
interest. How much interest will Samir need to pay?
$1656

c. What will be the amount of each monthly payment that Samir makes?

Need help with c), I don't understand the question :/

Answer 1

How much will he pay each month?

(4600 + 1656) / 48 = ?

Answer 2

omg, im so stupid, i thought it meant how much money he makes.. thanks so much

Answer 3

:-) You are very welcome.

Answer 4

a) is correct
b) banks do not lend out money for 4 years at simple interest, they use compound interest.
You will have to answer c) first, that is , find the monthly payment

c)
i = .09/12 = .0075
n = 4(12) = 48
paym = ?

4600 = paym( 1 - 1.0075^-48)/.0075
you should get $114.47

b) the "invalid" calculation they expect is probably:
48(114.47) - 4600
= 894.62

Here is the reason why the total simple interest of 1656 is incorrect:
As you are paying off the loan , the outstanding balance keeps decreasing, thus the interest keeps shrinking while your actual repayment keeps increasing.
e.g. of the first payment of 114.47, the interest is
6400(.0075) or $48 and the actual repayment is $66.47

when you get to the last month's balance it would be
$113.62 (don't worry how I got that)
the interest on that would be .0075(113.62) or $0.85
giving us a final payment of 113.62 + .85 = $114.47

Notice the small amount of interest compared to the interest for the first payment.