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
Amar borrowed Rs. 10000 from Sachin at simple interest. After 4 years, Sachin received Rs. 5000 more than the amount given to Amar on loan. Find the rate of interest.
Simple interest accrued on the amount of Rs.14,000 is Rs. 1260 at the rate of 3 % per annum for t years. What would be the compound interest accrued on the same amount for the same years at 10 % per annum compounded annually?
Rishu deposited an amount of Rs. 950 at Compound Interest. The amount gets doubled of itself after 4 years. What will be the amount after 12 years?
Which of the following schemes of computing interest yields the maximum interest for a year?
On a certain sum, rate of interest per annum for the first two years is 4%. The rate of interest for next four years is 6% and for the next three years is 8%. If total simple interest earned at the end of 9 years is ₹ 1120, then the sum is:
