Question

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The interest on a sum of ₹ 12800 is being compounded annually at the rate of 7.5% per annum.Find the period for which the compound interest is ₹ 1992.

Answer 1

Solutions :-

Some of the abbreviations used in the solutions are :-

Principle = p
Time = t
Rate = r
Compound Interest = C.I
Amount = A

Given :

p = ₹ 12800
r = 7.5% p.a
C.I = ₹ 1992

Find the Amount :-

A = p + C.I
= ₹ (12800 + 1992)
= ₹ 14792

Find the Time :-

A = p (1 + r)^t
14792 = 12800 (1 + 7.5%)^t
14792 = 12800 (1 + 0.075)^t
14792 = 12800 (1.075)^t
14792/12800 = (1075/1000)^t
7396/6400 = (86/80)^t
(86/80)^2 = (86/80)^t
2 = t

Hence,
Time = 2 years

Answer 2

Solutions :-



We have,

Principle = p = ₹ 12800
Rate = r = 7.5% p.a
Compound Interest = C.I = ₹ 1992
Amount = A = ?
Period = t = ?



Find the Amount :-
A = p + C.I
= ₹ (12800 + 1992)
= ₹ 14792



Find the Time :-
By using Compound Interest formula

A = p (1 + r)^t

=> 14792 = 12800 (1 + 7.5%)^t
=> 14792 = 12800 (1 + 0.075)^t
=> 14792 = 12800 (1.075)^t
=> 14792/12800 = (1075/1000)^t
=> 7396/6400 = (86/80)^t
=> (86/80)^2 = (86/80)^t
=> 2 = t


Answer : Period = 2 years