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
- The difference between compound interest and simple interest on an amount of Rs.25,000 for 2 years is Rs.250. What is the rate of interest per annum? (In %)
- Increase in Debt-Equity ratio in a firm __________ to equity holders.
The difference between the compound interest and simple interest on a certain amount at 5%per annum for 2 years is Rs. 15.The principal amount is equal to :
Dhoni invested Rs 22000 at 12% simple interest per annum and Rs 15000 at 10% compound interest per annum, then find the total amount earned by him at the end of 2 years.
The difference between the compound interest and the simple interest on a sum of Rs. 8,000 for 2 years at the rate of 5% p.a. is:
