How long will it take to pay the loan back ?
Level
pending
I start repaying a loan of $ 65000. The first installment is $ 400 and the subsequent installments are $ 300 more than the previous month. After how many months can the entire loan amount be repaid ?
The answer is 20.
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1 solution
The Installments are paid the sequence
400 , 700, 1000, 1300....
So the sum of "n" terms of an Arithmetic Progression is n*(a + ( d)(n-1)/2) where a is the first term and "d" is the common difference of the Arithmetic Progression
We hence get 65000 = n (400 + 300 (n-1)/2) ,
1300 = n (8 + 3 (n-1)) = 5n + 3n^2 or 3n^2 + 5n -1300 = 0 factorizes as (3n + 65)(n-20) = 0 , as n > 0 , n = 20 or in other words the loan can be repaid in 20 months