A gentleman buys every year Bank’s cash certificates of value exceeding the last year’s purchase by ₹250. After 20 years, he finds the total

Question

A gentleman buys every year Bank’s cash certificates of value exceeding the last year’s purchase by ₹250. After 20 years, he finds the total value of purchased certificates by him is ₹72500. Find the value of the certificates purchased by him : (a) in the first year (b) in the 13th years.

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1 month 2021-08-18T04:07:03+00:00 1 Answer 0 views 0

Let the value of the certificates purchased in the first year be Rs.a.

The difference between the value of the certificates is Rs. 300(d=300).

Since, it follows Arithmetic progression the total value of the certificates after 20 years is given by

Sn = n/2 [2a−(n−1)d]= 20/2 [2a+19(300)]=8300

By simplifying we get 2a+5700=8300.

Therefore, a=Rs.1300.

The value of the certificates purchased by him in nth year =a+(n−1)d.

Therefore, the value of the certificates purchased by him in 13th year =1300+(13−1)300=Rs.4900.