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 :/
How much will he pay each month?
(4600 + 1656) / 48 = ?
omg, im so stupid, i thought it meant how much money he makes.. thanks so much
:-) You are very welcome.
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.
I can help you with question c) regarding the monthly payment that Samir needs to make for his car loan. To calculate the monthly payment, we will use a formula called the "Amortization Formula."
The formula for calculating the monthly payment (PMT) is:
PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments
Let's plug in the values given in the question to calculate the monthly payment for Samir:
Principal amount (P) = $4600 (loan amount after deducting the deposit)
Annual interest rate = 9%
Number of years = 4
Number of monthly payments (n) = 4 * 12 = 48
First, we need to calculate the monthly interest rate (r). We divide the annual interest rate by 12:
r = (9% / 100) / 12 = 0.0075
Next, we can substitute the values into the formula:
PMT = (4600 * 0.0075 * (1 + 0.0075)^48) / ((1 + 0.0075)^48 - 1)
PMT = (4600 * 0.0075 * 1.38684925) / (1.38684925 - 1)
PMT = 48.9990803814
Therefore, the monthly payment that Samir needs to make for his car loan is approximately $48.999, which we can round up to $49.
Please note that the above calculation does not include any additional fees or charges that might be applied by the bank or financing institution. It is always recommended to consult with the bank or lender for accurate repayment information.