# math of investment

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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 -

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 -

27523.60

• math of investment -

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 -

9765.25

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