Several homeowners in a nearby community have organized to protest against alleg
ID: 2735089 • Letter: S
Question
Several homeowners in a nearby community have organized to protest against alleged gouging on the part of a local lending institution. One resident presents his payment book as evidence. The resident has a 30-year, fixed rate loan at 6 percent interest for $200,000. He got the loan 10 years ago and has been making equal annual payments of $14,529.60 ever since. He observes that he has paid the lending company $145,296.00 yet his payment book indicates that the principal due on the loan has only declined by $33,345.40. He presents this as obvious proof of "gouging on the part of the money changers". Do you agree? Why, why not?
Explanation / Answer
To answer this, we first need to find out the remaining balance after the payments made in 10 years. This calculation is done below:
Formula: Remaining Loan balance after P months:
B = [L*(1 + r)n] – [P*((1 + r)n-1)/r)]
The amount you borrow is L, the interest rate per period is r, the number of payments done is n and payments per period is P.
L = $200,000
r = 6%
n = 10
P = $14,529.60
Remaining balance = [$200,000*(1+0.06)10 – [$14,529.60*((1+0.06)10 -1)/0.06)] = $166,657.90
Principal paid = $200,000 - $166,657.90 = $33,342.14 (Approx $33,345.40)
As we can see that the paid principal on the loan is the amount shown by the lending company, the company is not doing anything wrong.
Reason: When we make repayments toward any kind of loan, initially most of the part of repayment amount goes towards the interest payments & a little part towards the principal. As we keep on repaying, the principal amount goes down resulting lesser interest, which increases the proportion of payment towards principal.