Question

A sum of ₹ 2000 is invested at 4% simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of 30 year will be ____.

• A. ₹1200
• B. ₹ 2400
• C. ₹ 4800
• D. No AP is formed

Answer 1

The correct option is B ₹ 2400

Given, sum = ₹ 2000
Interest = 4%
$SIfor1year,SI=\frac{P\times R\times T_1}{100}=\frac{2000\times 4\times 1}{100}=₹80SIfor2years,SI=\frac{P\times R\times T_2}{100}=\frac{2000\times 4\times 2}{100}=₹160SIfor3years,SI=\frac{P\times R\times T_3}{100}=\frac{2000\times 4\times 3}{100}=₹240$
and so on.
So, SI forms an AP
80, 160, 240, 320, . .
with a = 80 and d = 80
$\therefore$ Total interest for 30 years,
$T_{30}$ = a + (n - 1) d
= 80 + (30 - 1)80
= 80(30) = ₹ 2400
$\therefore$ Total interest for 30 years is ₹ 2400