(a) To calculate the interest earned by saving the rupees in Bank A and Bank B, we need to use the formula for compound interest:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
P = Principal amount (in this case, Rs 80,000)
r = Annual interest rate (given as 12% for Bank A)
n = Number of compounding periods per year (in this case, 1, as it is yearly compound interest)
t = Number of years (in this case, 2)
Using this formula, we can calculate the interest earned in each bank:
For Bank A (Yearly Compound Interest):
Interest = 80,000(1 + 0.12/1)^(1*2) - 80,000
For Bank B (Half-Yearly Compound Interest):
First, we need to convert the annual interest rate to a half-yearly rate:
Effective rate for every 6 months = (1 + Annual Interest Rate)^(1/2) - 1
Effective rate for every 6 months = (1 + 0.10)^(1/2) - 1
Then, we can calculate the interest using the formula for half-yearly compound interest:
Interest = 80,000(1 + 0.10/2)^(2*2) - 80,000
(b) In order to determine in which bank to save money, we need to compare the interest earned in both Bank A and Bank B.
Based on the calculations done above, we can compare the interest earned in each bank. The bank that provides the higher interest will be the preferred option for saving money.
Therefore, after calculating the interest earned, we can compare the values to decide which bank to choose. The one offering the higher interest would be the recommended option for saving money.
Note: The specific values for the interest earned in Bank A and Bank B can be calculated using the provided formulas and the given interest rates.