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 find the interest at the end of the 30th year.
(3 Marks)

Answer 1

Given, sum = ₹ 2000
Interest = 4% (0.5 Mark)
SI for 1 yr,
$SI=\frac{P\times R\times T_1}{100}=\frac{2000\times 4\times 1}{100}=₹80$
(0.5 Mark)

SI for 2 yr,
$SI=\frac{P\times R\times T_2}{100}=\frac{2000\times 4\times 2}{100}=₹160$
(0.5 Mark)
SI for 3 yr,
$SI=\frac{P\times R\times T_3}{100}=\frac{2000\times 4\times 3}{100}=₹240$
and so on. (0.5 Mark)
So, SI forms an AP
80, 160, 240, 320, . .
with a = 80 and d = 80
$\therefore$ Interest for 30 year,
$T_{30}$ = a + (n - 1) d
= 80 + (30 - 1)80
= 80(30) = ₹ 2400 (1 Mark)