To find the initial amount deposited into the saving account, we can use the formula for simple interest:
\[ A = P + I \]
where:
- \( A \) is the total amount in the account (balance),
- \( P \) is the principal or initial amount deposited,
- \( I \) is the interest earned.
The interest \( I \) can be calculated using the formula:
\[ I = P \times r \times t \]
where:
- \( r \) is the rate of interest (as a decimal),
- \( t \) is the time the money is invested or borrowed for (in years).
In this case:
- \( A = 20,400 \) Birr
- \( r = 8% = 0.08 \)
- \( t = 3 \) months = \( \frac{3}{12} = \frac{1}{4} \) years
Now, substituting \( t \) into the interest formula:
\[ I = P \times 0.08 \times \frac{1}{4} = P \times 0.02 \]
Now, we can plug \( I \) back into the equation for \( A \):
\[ A = P + I \] \[ 20,400 = P + P \times 0.02 \] \[ 20,400 = P (1 + 0.02) \] \[ 20,400 = P \times 1.02 \]
To find \( P \), we divide both sides by \( 1.02 \):
\[ P = \frac{20,400}{1.02} \] \[ P = 20,000 \]
So, the initial amount deposited was Birr 20,000.
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