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A man invests ₹ 5000 for three years at a certain rate of interest, compounded annually. At the end of

one year it amounts to ₹ 5600. Calculate:

(i) the rate of interest per annum

(ii) the interest accrued in the second year.

(iii) the amount at the end of the third year.

Answer:

Compound interest is calculated on the principal and interest accrued over a period of time. It differs from simple interest in that interest is not added to the principal when computing interest over time.

It is given that

Principal = ₹ 5000

Consider r% p.a. as the rate of interest

(i) We know that

At the end of one year

Interest = Prt/100

Substituting the values

= (5000 × r × 1)/ 100

= 50r

Here

Amount = 5000 + 50r

We can write it as

5000 + 50r = 5600

By further calculation

50r = 5600 – 5000 = 600

So we get

r = 600/50 = 12

Hence, the rate of interest is 12% p.a.

(ii) We know that

Interest for the second year = (5600 × 12 × 1)/ 100

= ₹ 672

So the amount at the end of the second year = 5600 + 672

= ₹ 6272

(iii) We know that

Interest for the third year = (6272 × 12 × 1)/ 100

= ₹ 752.64

So the amount after the third year = 6272 + 752.6

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