Question

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually

Answer 1

Hint: The principal amount deposited, the compound interest are given which can be used to calculate the amount as:
Amount = Principal + Interest
Then by using the formula for amount, we can calculate the time.
 $ {\text{Amount = P}}{\left( {1 + \dfrac{R}{{100}}} \right)^t} $
where,
P is principal, R is rate and t (in years) is the time for the compound interest.

Complete step-by-step answer:
Given:
Principal (P) = Rs. 1500
Rate (R) = 10%
Compound Interest (C.I) = Rs. 496.50
Now,
Amount = Principal + Interest
Amount = 1500 + 496.50 =1996.50
Substituting these values in the formula of amount to calculate t, we get:
 $ {\text{Amount = P}}{\left( {1 + \dfrac{R}{{100}}} \right)^t} $
 $ {\text{1996}}{\text{.50 = 1500}}{\left( {1 + \dfrac{{10}}{{100}}} \right)^t} $
 $ \dfrac{{1996.50}}{{1500}} = {\left( {\dfrac{{110}}{{100}}} \right)^t}{\text{ }}[{\text{Taking LCM]}} $
 $ \dfrac{{1331}}{{1000}} = {\left( {\dfrac{{11}}{{10}}} \right)^t} $
This can be written as:
 $ {\left( {\dfrac{{11}}{{10}}} \right)^3} = {\left( {\dfrac{{11}}{{10}}} \right)^t} $

It can be seen that both the fractions are the same and this implies that the value of their powers will also be the same.
Therefore, t = 3
Thus, the amount of Rs. 1500 will yield Rs. 496.50 as compound interest at 10% per annum compounded annually in 3 yrs.

Note: Compound interest can be compounded half yearly as well and in such a case, while proceeding with the questions, we stick to the same formula for amount but double the time (t x 2) and half the rate \[\left( {\dfrac{R}{2}} \right)\].
When principal and amount are given, compound interest can be calculated as:
Interest = Amount – Principal [As Amount = Principal + Interest]