Jane made a down payment of 1500 dollars toward the purchase of a car. To pay the balance of the purchase price, she has secured a loan from her bank at the nominal rate of 5.8 percent per year compounded monthly. Under the terms of her finance agreement, she is required to to make payments of 100 dollars per month for 36 months.
a) What is the cash price of the car?
b)How much, in total, will Jane spend on interest charges?
I can't seem to apply the loan payment formula ! Help please? Thanks
n = 36
i = .058/12 = .0048333... ( store that in calculator's memory)
Present value of her loan
= 100( 1 - (1+.058/12)^-36)/(.058/12)
= $3296.91
plus her downpayment of $1500
would give a present value of $4796.91
To find the cash price of the car, you need to find the present value of the loan payments.
In this case, Jane is making payments of $100 per month for 36 months, with a nominal interest rate of 5.8% per year compounded monthly.
To calculate the present value of the loan payments, you can use the formula for the present value of an ordinary annuity:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value (cash price of the car)
PMT = Payment per period ($100 per month)
r = Periodic interest rate (5.8% per year / 12 months = 0.00483 per month)
n = Total number of periods (36 months)
Now let's calculate:
a) Cash price of the car:
PV = $100 * (1 - (1 + 0.00483)^(-36)) / 0.00483
PV ≈ $3,084.51
Therefore, the cash price of the car is approximately $3,084.51.
b) To find the total interest charges, subtract the down payment from the total amount paid over the loan term:
Total interest charges = (Total payments) - (Down payment)
Total interest charges = ($100 * 36) - $1500
Total interest charges = $3600 - $1500
Total interest charges = $2100
Therefore, Jane will spend a total of $2100 on interest charges.