Final answer:
The student's question involves setting up and solving a system of equations to determine the account balances for a savings account and a fixed deposit account based on given interest rates and additional interest earned. Suntali deposited Rs 5,000 in her savings account and Rs 4,000 in her fixed deposit account.
Step-by-step explanation:
To determine how much Suntali deposited in each of her saving and fixed deposit accounts, we need to set up a system of equations based on the information provided. Let's denote the amount deposited in the saving account as S and the amount in the fixed deposit account as F. The total deposited amount is Rs 9,000, which gives us our first equation:
1) S + F = 9000
Next, we will create an equation for the interest accrued on each account after one year. The saving account has a 5% annual compound interest rate, so Suntali earns 0.05S in interest from this account. Her fixed deposit account has a 10% interest rate compounded semi-annually, which means after six months, the interest rate is 5%. Thus, the equation is as follows:
F x 1.052 - F - 0.05S = 160
2) F(1.052 - 1) - 0.05S = 160
Using the first equation to solve for S (S = 9000 - F) and substituting into the second equation gives us:
F(1.1025 - 1) - 0.05(9000 - F) = 160
Expanding and solving this equation:
0.1025F - 450 + 0.05F = 160
0.1525F = 610
F ≈ 4000
Thus, S = 9000 - 4000 = 5000.
This means Suntali deposited Rs 5,000 in her saving account and Rs 4,000 in her fixed deposit account.