payments problem?

Question

Mary has just purchased a car for AED 124,000. She paid 50% as a down payment and borrowed the remainder from the bank at a discount rate of 12% compounded monthly over 20 months.

1. How much does Maryam pay the bank each month? 3435.75

2. How much is her last payment? 3435.16

3. How much is paid in total for the car? 130714.41

4. How much of that is interest? 6714.41

I only figured out how to get the first one... the others, i dont.. so i need some help on it ^^!

Answer 1

1) the 12% compounded monthly means that the interest rate per month is 0.12/12 = 0.01.

Also, the balance to be paid in 20 months is 50% of 124000 or 62000.

To find the monthly payments, use R = 62000*0.01/(1-1.01^-20). This came from equating the present value of monthly payments with the balance of 62000:

Balance = R x (1 - (1+i)^-n)/i ,
where i = 0.01 (rate) , n = 20 (months)
therefore, R = 3,435.75

2) The payments are the same each month, so the last payment is 3,435.75.

3) The total monthly payments is 20x3,435.75 = 68,715
when we add the down payment, this becomes
130,715

4) the interest paid is the difference between the cash price of the car and the total payments (#3):

130, 715 - 124,000 = 6,715

The difference in our answers is due to rounding errors. I used a spreadsheet, so mine is more accurate.

Also, do not forget to put the currency sign on your answers.
e.g. AED 6,715 to prevent possible deductions.

Answer 2

1. 62000 = X[1 - 1/(1.01)^20]/.01 = 18.04555X, so X = 3435.75

2. Payments should be the same; any difference is rounding.

3. 62000 + 20 x 3435.75 = 130715

4. 130715 - 124000 = 6715.

Answer 3

4 is easy. Total paid is 130714.41 and if we subtract 124,000 we get that 6714.41