3 months
To find out in what duration of time ₹3300 will become ₹3399 at 12% per annum interest compounded quarterly, we will use the compound interest formula:
\(A = P \left(1 + \frac{r}{n}\right)^{nt}\)
Where:
- \(A\) = the final amount = ₹3399
- \(P\) = the principal amount = ₹3300
- \(r\) = annual interest rate = 12% = 0.12
- \(n\) = number of times interest is compounded per year = 4 (quarterly)
- \(t\) = the time in years = ?
Substituting the known values into the formula:
\(3399 = 3300 \left(1 + \frac{0.12}{4}\right)^{4t}\)
\(3399 = 3300 \left(1 + 0.03\right)^{4t}\)
\(3399 = 3300 \times (1.03)^{4t}\)
To find \(4t\), divide both sides by 3300:
\(\frac{3399}{3300} = (1.03)^{4t}\)
\(1.03 = (1.03)^{4t}\)
Since \(1.03 = (1.03)^1\), we have:
\(4t = 1\)
Now solving for \(t\):
\(t = \frac{1}{4} \text{ year} = 3 \text{ months}\)
The correct answer is that the duration of time required is 3 months.
Important Questions from Interest
Three years ago, the value of a flat was Rs. 65,00,000. Its value depreciated at the rate of 5%, 4% and 3% at the end of the first, the second and the third year, respectively. What is its present value?
An electric bulb was bought at Rs. 4200 Its value depreciates at the rate of 8% per annum Its value after one year will be:
What is the amount of money invested after 4 years at the rate of simple interest rate of 13% per annum invested at 4,950 rupees. (In rupees)
A certain sum of money amounts to \(\frac{3}{2}\) of itself in 2 years applying simple interest. Find the rate of simple interest per annum.
A sum of Rs. 2000 will become Rs. 2400 in 12 months at some rate of simple interest. Find the rate of interest per annum.
