Find the compound interest on ₹5,70,000 for 1.5 years at 10% per annum compounded half-yearly.
₹89,846.25
To find the compound interest on ₹5,70,000 for 1.5 years at an interest rate of 10% per annum compounded half-yearly, we can use the formula for compound interest:
\(A = P \left(1 + \frac{r/n}{100}\right)^{nt}\)
where:
- A is the amount after time t.
- P is the principal amount (₹5,70,000).
- r is the annual interest rate (10%).
- n is the number of times interest applied per time period (2 for half-yearly).
- t is the time the money is invested for in years (1.5 years).
First, convert the time period into the number of compounding periods:
\(t = 1.5 \ \text{years} = 3 \ \text{half-year periods}\)
Calculate the compound amount using the provided values:
\(A = 570000 \left(1 + \frac{10/2}{100}\right)^{3}\)
\(A = 570000 \left(1 + 0.05\right)^{3}\)
\(A = 570000 (1.05)^{3}\)
Now compute \((1.05)^3\):
\((1.05)^3 = 1.157625\)
Therefore, the amount \(A\) is:
\(A = 570000 \times 1.157625 = 659846.25\)
The compound interest is given by:
\(CI = A - P = 659846.25 - 570000 = 89846.25\)
Thus, the compound interest after 1.5 years is ₹89,846.25.
The correct answer is ₹89,846.25.
Similar Questions
In how many years will a sum of ₹16,000 at 10% per annum compounded semi-annually become ₹18,522?
If sum of Rs. 1000 amount to Rs. 1331 in 3 years, compounded annually. Then, find rate of interest per annum?
Find the compound interest on Rs. 62500 at 21% per annum for \(1\frac{1}{2}\) years compounded half yearly.
Consider the given question and decide which of the following statements is sufficient to answer the question.
X took a loan from Y on compound interest. Find the rate per annum?
Statements:
1. After 3 years, X paid Rs. 500 as interest.
2. After 3 years, X paid Rs. 1,500 to clear his loan with Y.
Shams invested Rs. 4000 at 10% per annum compound interest. After n years, Shams received Rs. 1324 more, Find the value of n.
If Rs. 2,000 is invested at the rate of 20% per annum, compounded half yearly, then find the amount after 18 months.
Important Questions from Compound Interest
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
