A person invests ₹ 10000 for two years at a certain rate of interest, compounded annually. At the end of one year this sum amounts to ₹ 11200. Calculate:
(i) the rate of interest per annum.
(ii) the amount at the end of second year.
Solution:
It is given that
Principal (P) = ₹ 10,000
Period (T) = 1 year
Sum amount (A) = ₹ 11,200
Rate of interest = ?
(i) We know that
Interest (I) = 11200 – 10000 = ₹ 1200
So the rate of interest
R = (I × 100)/ (P × T)
Substituting the values
R = (1200 × 100)/ (10000 × 1)
So we get
R = 12% p.a.
Therefore, the rate of interest per annum is 12% p.a.
(ii) We know that
Period (T) = 2 years
Rate of interest (R) = 12% p.a.
Here
A = P (1 + R/100)t
Substituting the values
A = 10000 (1 + 12/100)2
By further calculation
A = 10000 (28/25)2
We can write it as
A = 10000 × 28/25 × 28/25
So we get
A = 16 × 28 × 28
A = ₹ 12544
Therefore, the amount at the end of second year is ₹ 12544.
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