Question #de9db

1 Answer
Jan 1, 2018

Answer:

Total interst is #6840# dollars.

Explanation:

To begin with, let's see how much the company will pay in the first two months.

[First month]
Interest: #$36000 * 0.02 = $720#
Principal: #$2000#
Total: #$2720#

[Second month]
Interest: #$34000 * 0.02 = $680#
Principal: #$2000#
Total: #$2680#

How about the last month?
[Last(18th) month]
Interest: #$2000 * 0.02 = $40#
Principal: #$2000#
Total: #$2040#

Then, what is the sum of the interest?
#720,680,...,40# is an arithmetic progression.
The sum of an arithmetic progression is
#S=1/2 n(a_1+a_n)# ,where
#n#: number of terms
#a_1#: first term
#a_n#: last term.

Substitute #n=18, a_1=720, a_n=40# to this formula.
#S=1/2 *18*(720+40)=6840#

Thus, the total interst the company has to pay is #$6840#.