Question 1109126: The price of a new car is $12,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 8%/year compounded monthly. (Round your answers to the nearest cent.)
(a) What monthly payment will she be required to make if the car is financed over a period of 60 months? Over a period of 72 months?
(b) What will the interest charges be if she elects the 60-month plan? The 72-month plan?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! price of the car is 12,000.
down payment is 25%.
finance rate is 8% compounded monthly.
(a) What monthly payment will she be required to make if the car is financed over a period of 60 months? Over a period of 72 months?
(b) What will the interest charges be if she elects the 60-month plan? The 72-month plan?
using TI-BA-II, you would do the following:
for 60 month loan:
PV = .75 * 12,000 = 9,000
FV = 0
I/Y = 8% / 12
N = 60
calculate PMT to get:
PMT = 182.4875486 per month
for 72 month loan:
PV = .75 * 12,000 = 9,000
FV = 0
I/Y = 8% / 12
N = 72
calculate PMT to get:
PMT = 157.7991655 per month
in the calculator:
the 9,000 is entered as positive because it's money that the bank gave to you.
the monthly payment is shown as negative because it's money you gave to the bank.
with the 60 month loan, your payment is 182.4875486 per month.
multiply this payment by 60 months and the total you paid to the bank is 10,949.25292.
subtract 9,000 from this, and the interest you paid is 1,949.252916.
with the 72 month loan, your payment is 157.7991655 per month.
multiply this payment by 72 months and the total you paid to the bank is 11,361.53992.
subtract 9,000 from this, and the interest you paid is 2,361.539917.
rounded to 2 decimal places, you get:
60 month loan pays 182.49 per month with total interest of 1,949.25.
72 month loan pays 157.80 per month with total interest of 2,361.54.
you can do this with formulas as well.
the formula you would use is:
ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.
this formula was taken from https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9
using this formula on the 60 month loan, a = (p*r)/(1-(1/(1+r)^n)) becomes:
a = (9000*.08/12)/(1-(1/(1+.08/12)^60)), resulting in:
a = 182.4875486.
using this formula on the 72 month loan, a = (p*r)/(1-(1/(1+r)^n)) becomes:
a = (9000*.08/12)/(1-(1/(1+.08/12)^72)), resulting in:
a = 157.7991655.
you enter the interest rate as a rate, not a percent.
8% divided by 100 = .08.
you need to make sure you enter the parentheses in your calculator exactly as shown.
otherwise, you may not be able to duplicate the answer that the financial calculator gave you.
if you wish to do this using an online financial calculator, then one such calculator that can be used is found at https://arachnoid.com/finance/
that calculator works the same as the TI-BA-II, but it does some rounding on the inputs and outputs, so the answer is less detailed as with the TI-BA-II.
using that calculator, i got:
60 month loan monthly payment is 182.49
72 month loan monthly payment is 157.80
calculating total interest based on that result, i would have gotten.
total interest on 60 month loan is 60 * 182.49 - 9000 = 19,49.40
total interest on 72 month loan is 72 * 157.80 - 9000 = 2,361.60
the difference between that and what i got above using the TI-BA-II is intermediate rounding of results.
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