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in Arithmetic Progression by (41.6k points)
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A sum of Rs.1,000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests for 1st, 2nd and 3rd years form an A.P. ? If so, find the total interest to be paid for 30 years making the use of this fact.

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Sum invested = P = Rs. 1000 

Rate of interest = R = 8% 

Time of investment = 1 year 

∴ Amount of interest (simple)

So the amount of interest for the years 1, 2, 3, …………….are 

80, 160, 240,….. are in an A.P. 

In which the first term (a) 5= 80 

Common difference (d) = a2 – a1 

= 160 – 80 = 80

∴ The amount of interest to be paid in 30 years of time = S30 

Sn = j [2a + (n- l)d] 

\(\frac{n}{2}\) [2(80) + (30 – 1) 80] 

= 15[160 + 29(80)] 

= 15[160 + 2320] 

= 2480 × 15 – Rs.37200 

∴ Rs.37200 will be paid towards interest for 30 years.

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