Find the amount after 3 years at the above rate of compound interest.

At what rate percent p.a. compound interest would ₹ 80000 amounts to ₹ 88200 in two years, interest being compounded yearly. Also find the amount after 3 years at the above rate of compound interest.

Solution:

It is given that
Principal (P) = ₹ 80000
Amount (A) = ₹ 88200
Period (n) = 2 years
Consider r% per annum as the rate of interest percent
We know that
A/P = (1 + r/100)n
Substituting the values
88200/80000 = (1 + r/100)2
By further calculation
(1 + r/100)2 = 441/400 = (21/20)2
So we get
1 + r/100 = 21/20
r/100 = 21/20 – 1 = 1/20
By cross multiplication
r = 1/20 × 100 = 5
Hence, the rate of interest is 5% per annum.

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