SOLUTION: A family borrowed $72,000 to buy a house. The loan was at 6.1% and for 25 years. The monthly payments were $468.31 each. (See Example 6.) (a) How much of the first month's payment

Question 1194571: A family borrowed $72,000 to buy a house. The loan was at 6.1% and for 25 years. The monthly payments were $468.31 each. (See Example 6.)
(a) How much of the first month's payment was interest, and how much was principal?
interest $
principal $
(b) What was the total amount paid over the 25 years?
$
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Part (a)

The annual interest rate is 6.1%
The monthly rate is (6.1%)/12 = 0.50833333333333% approximately.
The 3's go on forever.

This percentage then converts to the decimal form 0.0050833333333333
Either divide by 100, or simply move the decimal point over two spots to the left.

Multiply this approximate decimal value with the current balance.
72,000*0.0050833333333333 = 366
This result is the interest for the first month.

Yes the interest portion is quite high. It's common to have high interest payments at first.
As time goes on, the interest steadily goes down as the principal goes up.
The reason for this is because the balance will go down.

Subtract the interest from the monthly payment to compute the principal
468.31 - 366 = 102.31

Answers:
Interest = $366
Principal = $102.31

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Part (b)

1 year = 12 months
25*1 year = 25*12 months
25 years = 300 months

If you did a monthly payment of $468.31 for 300 months, then you will have paid back a total of 468.31*300 = 140,493 dollars.

Answer: $140,493

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