Wednesday
May 4, 2016

# Homework Help: math

Posted by jason on Thursday, August 3, 2006 at 8:36pm.

If you paid 2,000 a month or 24,000 a year on 200,000 dollars at 5.00% what formula would you use to calculate the interest paid? Thanks

The first year you'd pay \$10,000 (.05 x \$200,000) in interest. The remaining \$14,000 of your payment would be applied to the principle.

So -- in the second year your mortgage would be \$186,000. At 5%, your interest payment would be \$9,300. Subtract \$9,300 from \$24,000 to find how much is applied to the principle the second year.

Continue this calculation.

An example of how the loan payyment is derived ijn the first place will lead you to the method for calculating your interest.

What is the periodic payment required to retire a debt of P dollars in n periods (months or years) if payments start at the end of the first period and bear I% interest compounded periodically?
For this typical loan payment calculation, R = Pi/[1 - (1 +i)^(-n)] where R = the periodic payment, P = the amount borrowed, n = the number of payment periods, and i = I/100.
Example: What is the annual payment required to retire a loan of \$10,000 over a period of 5 years at an annual interest rate of 8%? Here, P = 10,000, n = 5, and i = .08 resulting in

R = 10000(.08)/[1 - (1.08)^-5] = \$2504.56 per year

The total amount paid back becomes 5(2504.56) = \$12,522.82 meaning that the use of the money cost the borrower \$2,522.82. It is worthy of note that most loans are paid on a monthly basis. The significance of this to the borrower is that he is paying the money back more often, thus reducing the outstanding balance more rapidly. The effect of this is to reduce the total amount paid for the use of the money. Here, P = 10,000, n = 60, and i = .006666 resulting in

R = 10000(.006666)/[1.006666)^-60] = \$202.76 per month.

The total amount paid back becomes 202.76(60) = \$12,165.60, a saving of \$357.22 by paying monthly.