A saving account opened 3 months ago now has a balance of Birr 20,400. If the bank pays 8% simple interest, how much money was deposited?

1 answer

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.