A 30year loan is to be repaid with equal installments at the

A 30-year loan is to be repaid with equal installments at the end of each year. The amount of interest in the 7th installment is $100 and the amount of interest in the 19th installment is $80. Find the amount of interest paid in the 25th installment.

Solution

We can solve this sum by using Arthritic Progression.
The nth term of an AP series is= a+(n-1) d, where a denotes the first term, n denotes the number of terms and d denotes the common difference.
Here, 7th term: a+(7-1)d=a+6d
19th term=a+18d
Now,
According to question,
a+6d=100 ...... (i)
a+18d=80 ...... (ii)
Now, (i) - (ii) => -6d=20
or, d=(-20/6) = (-10/3)
Now substituting the value of d in equation (i), we get
a+6(-10/3)=100
or, a=120
Now, the 25th installment = a+(25-1) d
= 120 +(24)(-10/3)
=120+(-80)
=40
Hence, 25th installment =$40