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.
Solution:
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 second year = 5600 + 672
= ₹ 6272
(iii) We know that
Interest for the third year = (6272 × 12 × 1)/ 100
= ₹ 752.64
So the amount after third year = 6272 + 752.64
= ₹ 7024.64
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