Sure, Sabita has deposited Rs. 1,50,000 in a bank that offers a yearly interest rate of 6%. We are interested in calculating the compound amount as well as the compound interest after 2 years and 6 months.
Here's a step-by-step solution for the problem:
### Step-by-Step Solution:
1. Principal Amount (P):
The initial amount deposited by Sabita is Rs. 1,50,000.
2. Rate of Interest (R):
The yearly interest rate is 6%, which can be written as 0.06 in decimal form.
3. Time (T):
The total time period for which the amount is invested is 2 years and 6 months.
- Convert the 6 months into years: 6 months = 6/12 = 0.5 years.
- Therefore, the total time T = 2 + 0.5 = 2.5 years.
4. Compound Amount (A):
The compound amount can be calculated using the formula:
[tex]\[
A = P \left(1 + \frac{R}{1}\right)^{1 \cdot T}
\][/tex]
In this case, the interest is compounded annually (n = 1), so the formula simplifies to:
[tex]\[
A = P (1 + R)^T
\][/tex]
Plugging in the values:
[tex]\[
A = 150000 \times (1 + 0.06)^{2.5}
\][/tex]
5. Calculating the Compound Amount:
Let’s compute the value:
[tex]\[
A = 150000 \times (1.06)^{2.5}
\][/tex]
6. Compound Amount:
- After calculation, the compound amount (A) is found to be approximately Rs. 1,73,522.55.
7. Compound Interest (CI):
The compound interest can be found by subtracting the principal amount from the compound amount:
[tex]\[
CI = A - P
\][/tex]
[tex]\[
CI = 173522.55 - 150000
\][/tex]
8. Compound Interest:
- After calculation, the compound interest is approximately Rs. 23,522.55.
### Summary of Results:
(i) The compound amount Sabita will have after 2 years and 6 months is approximately Rs. 1,73,522.55.
(ii) The compound interest she will earn in 2 years and 6 months is approximately Rs. 23,522.55.
