SOLUTION: A cumulative deposit account of monthly installment of rs. 3600 at 9% p.a. simple interest earns an interest of rs. 17982. Find the number of installment paid.

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Question 1105355: A cumulative deposit account of monthly installment of rs. 3600 at 9% p.a. simple interest earns an interest of rs. 17982. Find the number of installment paid.
Answer by greenestamps(13195) About Me  (Show Source):
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If the monthly deposit amount is rs. 3600 and the interest is simple interest at 9% per year, then the amount of interest on each deposit each month is
rs. 3600*(.09/12) = rs. 27

If n is the number of deposits that are made, then the total amount of interest earned on the first deposit is 27(n); the total amount of interest on the second deposit is 27(n-1);...; the total amount of interest on the next-to-last deposit is 27(2), and the total amount of interest on the last deposit is 27(1).

Then the total amount of interest on all the deposits is
27(n+(n-1)+...+2+1) = 27*((n(n+1)/2)

Since the total amount of interest is rs. 17982,
27%28n%28n%2B1%29%2F2%29+=+17982
n%28n%2B1%29+=+2%2A17982%2F27+=+1332

Any of various methods will lead to 36%2A37=1332, so the number of deposits n is 36.