Jim made a down payment of 1000 dollars toward the purchase of a car. To pay the balance of the purchase price, he has secured a loan from his bank at the nominal rate of 5.1 percent per year compounded monthly. Under the terms of his finance agreement, he is required to to make payments of 300 dollars per month for 36 months.
What is the cash price of the car?
How much, in total, will Jim spend on interest charges?
I need help on the second part of the question :/
To find the cash price of the car, we can start by subtracting the down payment from the total amount that needs to be paid through the loan.
Total loan amount = Total number of payments * Monthly payment
Total loan amount = 36 * $300 = $10,800
Cash price of the car = Total loan amount + Down payment
Cash price of the car = $10,800 + $1000 = $11,800
Therefore, the cash price of the car is $11,800.
To find the total interest charges, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan (total amount to be paid)
P = the principal amount (loan amount)
r = annual nominal interest rate (5.1%)
n = number of times the interest is compounded per year (12, since the interest is compounded monthly)
t = number of years (36 months / 12 months per year = 3 years)
Plugging in the values, we have:
A = $10,800
P = $10,000 (loan amount, obtained by subtracting the down payment)
r = 0.051 (annual nominal interest rate of 5.1%, expressed as a decimal)
n = 12
t = 3
$10,800 = $10,000 (1 + 0.051/12)^(12*3)
Now we can solve for the future value (A) and subtract the principal amount (P) to find the total interest charges.
$10,800 - $10,000 = $800
Therefore, Jim will spend a total of $800 on interest charges.