Pre-Calculus help!?

Question

Assume that you buy a DVD television for $900 and agree to pay for it in 18 equal monthly payments at 1.5% interest per month on the unpaid balance
1) how much are the payments?
2) how much interest is paid?

Answer 1

1) Amount borrowed = $900
Let monthly repayments be $M

Then after 1st month
Amount owing ($) = Interest added to amount owing less monthly payment
= 900(1 + 0.015) - M

After 2nd month
Amount owing ($) = interest added to amount owing less monthly payment
=(900(1.015) - M)(1.015) - M
= 900(1.015)² - M(1.015) - M

After 3rd Month
Amount owing ($) = interest added to amount owing less monthly payment
= (900(1.015)² - 1.015M - M)(1.015) - M
= 900(1.015)³ - M(1.015)² - M(1.015) - M

After 18th month
Amount owing ($) = interest added to amount owing less monthly payment
= 900(1.015)^18 - M(1.015)^17 - ... - M(1.015)³ - M(1.015)² - M(1.015) - M
= 0 (as it has to now be repaid in full with this final repayment)

So 900(1.015)^18 = M(1.015)^17 + ... + M(1.015)³ + M(1.015)² + M(1.015) + M
= M((1.015)^18 - 1)/(1.015) - 1) (On summing a GP with a = M, r = 1.015 and n = 18)
So M = 900(1.015)^18 * 0.015/((1.015)^18 - 1)
= 900*0.015/(1 - 1.015^(-18))
= 57.43 (nearest cent)
So the monthly repayments are $57.43 per month

2) Total repaid = $57.43 * 18
= $1033.74
So total interest paid = $1033.74 - $900
= $233.74

(Flat interest rate = 233.74/900 x 100%
≈ 25.97% over the 18 months
That is equivalent to ~1.44% flat rate per month)

Answer 2

No. Kjaymen is wrong. You pay interest on the unpaid balance, not on the amount of each monthly payment. So in the first month, you pay interest on $900. At the end of the first month, some of your monthly payment goes first to paying the interest, and whatever is left after paying the interest i sused to reduce the balance.

In the second month, you pay interest on the new, lower, unpaid balance, and so on.

The monthly payment is $57.43. In the first month, the interest on $900 is $13.50. That leaves $43.93 left over to reduce the loan balance, so the balance for the second month is $856.07. At the end of the second month, less of your payment goes toward interest and more toward reducing your loan balance, until at the end your interest charges are very low and your payments go almost entirely to reducing the balance.

It's nice to see Wal agree with me on the amount of the monthly payment. The amount of interest paid is, as Wal says, the total of all payments minus $900.

Answer 3

A. Find the amount of each payment (without interest):
($900 / 18 months) = $50 per month

B. Add in the interest:
1.5% = 0.015. Therefore, (0.015*$50) = $0.75. So you pay $0.75 of interest every month. Now add the interest to the monthly payments to get your total payment per month: $50 + $0.75 = $50.75 for a total monthly payment.

C. Finally, find how much total interest is paid.
To do this, multiply the duration (18 months) by the monthly interest ($0.75)
(18*0.75) = $13.50

ANSWERS:
1. $50.75 every month
2. $13.50 total interest paid

Answer 4

The payments are, approximately $57.42520359 per month
which rounded off is $57.43

The total interest paid during that time is $133.65366460, RO
to $133.65

You did not ask for the simple interest rate, or other, so I leave that to you, if you need the data.

Answer 5

The last two answers were correct. I couldn't do it without my financial calulator, though! (Get one)