To calculate yearly compound interest for Bank A, which offers an 8% annual compound interest rate, we'll use the compound interest formula. Here is the step-by-step solution:
### Step-by-Step Solution:
Step 1: Identify the given values and variables.
- Principal amount (P) = Rs. 10,000
- Annual interest rate (r) = 8% = 0.08
- Number of times interest is compounded per year (n) = 1 (since it is compounded annually)
- Time period in years (t) = 1 year
Step 2: Write the compound interest formula.
The formula for compound interest is given by:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the future value of the investment, including interest,
- [tex]\( P \)[/tex] is the principal investment amount,
- [tex]\( r \)[/tex] is the annual interest rate (decimal),
- [tex]\( n \)[/tex] is the number of times the interest is compounded per year,
- [tex]\( t \)[/tex] is the time the money is invested for in years.
Step 3: Substitute the values into the formula.
[tex]\[ A = 10{,}000 \left(1 + \frac{0.08}{1}\right)^{1 \times 1} \][/tex]
Step 4: Simplify the expression inside the parentheses.
[tex]\[ 1 + \frac{0.08}{1} = 1 + 0.08 = 1.08 \][/tex]
Step 5: Raise the simplified base to the power of [tex]\( nt \)[/tex].
[tex]\[ A = 10{,}000 \left(1.08\right)^{1} \][/tex]
Step 6: Calculate the final amount.
[tex]\[ A = 10{,}000 \times 1.08 = 10{,}800 \][/tex]
Thus, the amount after one year, including the interest, will be [tex]\( Rs. 10{,}800 \)[/tex].
Conclusion:
Indira will have [tex]\( Rs. 10{,}800 \)[/tex] in her account after one year if she deposits [tex]\( Rs. 10{,}000 \)[/tex] in Bank A with an 8% annual compound interest rate.
