Question

At the rate of 16% per annum compounded quarterly, how long would it take for a
Sum of Rs. 200 to compound to Rs. 232.

Answer 1

Hint:To solve this question we should have knowledge that Rs.200 is principal amount Rs.232 is total amount, annual interest rate is 16% and number of times compounded per year is 4 and now just use the formula of compound interest and get the time.

Complete step-by-step answer:
We know the formula
\[A = P{\left( {1 + \dfrac{r}{n}} \right)^{n.t}}\]
Where
A = total amount
P = principal or amount of money deposited
r = annual interest rate
n = number of times compounded per year
t = time in years
we have given
P = Rs.200, r = 16%, n = 4, A = Rs.232
$\because A = P{\left( {1 + \dfrac{r}{n}} \right)^{n.t}}$
Putting all the values from given.
$232 = 200{\left( {1 + \dfrac{{0.16}}{4}} \right)^{4.t}}$
$\dfrac{{232}}{{200}} = {\left( {1.04} \right)^{4t}}$
$1.16 = {\left( {1.04} \right)^{4t}}$
When we put t =1 we get approx 1.16
$\therefore t = 1$ year.

Note: Whenever we get this type of question the key concept of solving is we have to understand all the terms of compound interest and we have to just figure out what is given and what has to be found out and after that use the formula of compound interest to get an answer.