Posted by **Icy** on Friday, February 22, 2008 at 8:36pm.

An article cost $29885. To buy this article, a down payment of $3420 is needed.If interest charged is 16% compunded quarterly, how much should be paid at the end of every 3 months for 1 year in order to payoff the balance?

please explain,i don't understand...thank you very much

- math of investment -
**drwls**, Friday, February 22, 2008 at 11:58pm
This is what is called an amortization problem. It is usually solved with a table or an iterating program. Here is a way to get the approximate answer directly. The principal due at the beginning is 29885-3420 = $26465. Over one year, with a declining balance, the average balance is $13232 and the interest on that amount over one year will be $2117.

It the loan is paid off in equal quarterly amounts, they must add up to 26465 + 2117 = $28582. The quarterly paymewnts should be 1/4 of that, or $7146.

Check:

Balance due at start (after down payment):

26465

After one quarter: add 1058.60 for interest due and subtract 7146 principal payment. Remaining balance = 20,377.60

After first quarter: add $815.10 interest and subract 7146 principl. Remaining balance = 14,046.70

After third quarter: add 561.87 interest and subtract 7146. Remaining balance = $7462.57

After fourth quarter: add $298.50 interest and subtract 7146. Remaining balance = $615.

For a second iteration, I would recommend adding $154 to each quarterly ayment, to get rid of the $615 deficit on the first attempt.

That makes the quarterly payment $7300 after one iteration. I end up overpaying $38 this way, so the third iterated answer is $10 less per quarter, or $7290.

- math of investment -
**tin**, Wednesday, November 12, 2008 at 6:28am
27523.60

- math of investment -
**drwls**, Saturday, February 23, 2008 at 12:02am
There is a handy amortization calculator at this web site:

http://www.yona.com/loan/

Enter the initial loan balance of 26465, the 16$ interest rate, and 4 quarterly payments.

Using it, with quarterly compounding you should get an exact loan payment of $7290.84

- math of investment -
**vincent**, Tuesday, November 18, 2008 at 12:42am
9765.25

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