Question

Sakura purchased ski equipment for $1,248 using a six-month deferred payment plan. The interest rate after the introductory period is 23.79%. A down payment of $175 is required as well as a minimum monthly payment of $95. What is the balance at the beginning of the seventh month if only the minimum payment is made during the introductory period?
I know the answer is $637.13, I just can't remember the math I did to get to that answer.

Same for this problem,

Forrest purchased a car for $20,640. He made a down payment of $2,440. He applied for a five-year installment loan with an interest rate of 10.4%. What is the total cost of the car after five years?

The answer is $25,857.40.

If someone could explain to me how to do the math to get to these answers that would be great, thank you. :)

Answer 1

Hi there

For the first question use the formula of the present value of annuity due
The formula is
Pv=pmt [(1-(1+r/k)^(-n))÷(r/k)]×(1+r/k)
Pv present value?
PMT monthly payment 95
R annual interest rate 0.2379
K compounded monthly 12
N time 7 months

Pv=95×((1−(1+0.2379÷12)^(
−7))÷(0.2379÷12))×(1+0.2379÷12)
=627.45 closed to 637.13 because the question mentioned the minimum monthly payment which is 95 while the exact monthly payment of 637.13
Is 96.47


The second question is the same and easier using the formula of the present value of annuity ordinary
First find the present value by subtracting the amount of down payment From the purchase price
20,640−2,440=18,200
Now find the monthly payment using the formula of
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Solve for pmt
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
Pv 18200
R 0.104
K 12
N 5 years

PMT=18,200÷((1−(1+0.104÷12)^(
−12×5))÷(0.104÷12))
=390.29

Total paid amount of monthly payment times number of months in a year times the term of the loan to get
390.29×12×5
=23,417.28

Finally how much you paid including down payment
23,417.28+2,440
=25,857.40. ..answer

Good luck!